有限雙邊理想基礎 · 脈衝 R02
本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261028-r02-finite-two-sided-ideal-foundations · 2026-10-14 · 100 題
1. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,2,4,6],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,2,7,4,1,6,3],[0,6,4,2,0,6,4,2],[0,7,6,5,4,3,2,1]],"subset":[0,1,2,4,6]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 1, 2, 4, 6], 0, 否, [[3, 1, 3], [5, 1, 5], [7, 1, 7]], [[1, 3, 3], [1, 5, 5], [1, 7, 7]], 否)
Wave4第二層核對=([0, 1, 2, 4, 6], 0, 否, [[3, 1, 3], [5, 1, 5], [7, 1, 7]], [[1, 3, 3], [1, 5, 5], [1, 7, 7]], 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
2. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,7,0,6],[2,3,4,5,7,6,1,0],[3,4,5,7,6,0,2,1],[4,5,7,6,0,1,3,2],[5,7,6,0,1,2,4,3],[6,0,1,2,3,4,7,5],[7,6,0,1,2,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,2,7,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,2,6,4,1,3,7],[0,6,7,5,4,3,1,2],[0,7,4,2,0,7,2,4]],"subset":[0,4]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 4], 0, 是, [], [], 是)
Wave4第二層核對=([0, 4], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
3. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,7,5,0],[2,3,4,6,5,0,7,1],[3,4,6,5,7,1,0,2],[4,6,5,7,0,2,1,3],[5,7,0,1,2,4,3,6],[6,5,7,0,1,3,2,4],[7,0,1,2,3,6,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,2,5],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,5,2],[0,6,2,7,4,5,1,3],[0,7,5,6,4,2,3,1]],"subset":[0]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0], 0, 是, [], [], 是)
Wave4第二層核對=([0], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
4. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,0,7,5],[2,3,4,6,7,1,5,0],[3,4,6,7,5,2,0,1],[4,6,7,5,0,3,1,2],[5,0,1,2,3,7,4,6],[6,7,5,0,1,4,2,3],[7,5,0,1,2,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,7,2,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,7,6,4,1,3,2],[0,6,2,5,4,3,1,7],[0,7,4,2,0,2,7,4]],"subset":[0,2,4,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 2, 4, 7], 0, 是, [], [], 是)
Wave4第二層核對=([0, 2, 4, 7], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
5. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,6,0,5],[2,3,4,7,5,0,1,6],[3,4,7,5,6,1,2,0],[4,7,5,6,0,2,3,1],[5,6,0,1,2,4,7,3],[6,0,1,2,3,7,5,4],[7,5,6,0,1,3,4,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,5,2],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,2,5],[0,6,5,7,4,2,1,3],[0,7,2,6,4,5,3,1]],"subset":[0,4]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 4], 0, 是, [], [], 是)
Wave4第二層核對=([0, 4], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
6. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,0,5,6],[2,3,4,7,6,1,0,5],[3,4,7,6,5,2,1,0],[4,7,6,5,0,3,2,1],[5,0,1,2,3,6,7,4],[6,5,0,1,2,7,4,3],[7,6,5,0,1,4,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,6,4,2],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,6,7,4,1,2,3],[0,6,4,2,0,2,4,6],[0,7,2,5,4,3,6,1]],"subset":[0,1,2,4,6]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 1, 2, 4, 6], 0, 否, [[3, 1, 3], [5, 1, 5], [7, 1, 7]], [[1, 3, 3], [1, 5, 5], [1, 7, 7]], 否)
Wave4第二層核對=([0, 1, 2, 4, 6], 0, 否, [[3, 1, 3], [5, 1, 5], [7, 1, 7]], [[1, 3, 3], [1, 5, 5], [1, 7, 7]], 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
7. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,4,7,0],[2,3,5,4,7,6,0,1],[3,5,4,6,0,7,1,2],[4,6,7,0,2,1,3,5],[5,4,6,7,1,0,2,3],[6,7,0,1,3,2,5,4],[7,0,1,2,5,3,4,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,2,0,5,6],[0,3,6,1,7,5,2,4],[0,4,2,7,1,5,6,3],[0,5,0,5,5,0,0,5],[0,6,5,2,6,0,5,2],[0,7,6,4,3,5,2,1]],"subset":[0,5]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 5], 0, 是, [], [], 是)
Wave4第二層核對=([0, 5], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
8. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,4,0,6],[2,3,5,4,6,7,1,0],[3,5,4,7,0,6,2,1],[4,7,6,0,2,1,5,3],[5,4,7,6,1,0,3,2],[6,0,1,2,5,3,7,4],[7,6,0,1,3,2,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,2,0,7,5],[0,3,7,1,6,5,4,2],[0,4,2,6,1,5,3,7],[0,5,0,5,5,0,5,0],[0,6,7,4,3,5,1,2],[0,7,5,2,7,0,2,5]],"subset":[0]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0], 0, 是, [], [], 是)
Wave4第二層核對=([0], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
9. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,6,4,0],[2,3,5,6,0,4,7,1],[3,5,6,4,1,7,0,2],[4,7,0,1,5,2,3,6],[5,6,4,7,2,0,1,3],[6,4,7,0,3,1,2,5],[7,0,1,2,6,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,2,4],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,4,2],[0,5,0,5,0,0,5,5],[0,6,2,7,4,5,1,3],[0,7,4,6,2,5,3,1]],"subset":[0,2,4,5]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 2, 4, 5], 0, 是, [], [], 是)
Wave4第二層核對=([0, 2, 4, 5], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
10. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,6,7,4],[2,3,5,6,1,7,4,0],[3,5,6,7,2,4,0,1],[4,0,1,2,7,3,5,6],[5,6,7,4,3,0,1,2],[6,7,4,0,5,1,2,3],[7,4,0,1,6,2,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,7,0,2,5],[0,3,7,1,6,5,4,2],[0,4,7,6,1,5,3,2],[0,5,0,5,5,0,5,0],[0,6,2,4,3,5,1,7],[0,7,5,2,2,0,7,5]],"subset":[0,5]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 5], 0, 是, [], [], 是)
Wave4第二層核對=([0, 5], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
11. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,7,0,4],[2,3,5,7,0,4,1,6],[3,5,7,4,1,6,2,0],[4,6,0,1,5,2,7,3],[5,7,4,6,2,0,3,1],[6,0,1,2,7,3,4,5],[7,4,6,0,3,1,5,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,4,2],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,2,4],[0,5,0,5,0,0,5,5],[0,6,4,7,2,5,1,3],[0,7,2,6,4,5,3,1]],"subset":[0,1,2,4,5]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 1, 2, 4, 5], 0, 否, [[3, 1, 3], [6, 1, 6], [7, 1, 7]], [[1, 3, 3], [1, 6, 6], [1, 7, 7]], 否)
Wave4第二層核對=([0, 1, 2, 4, 5], 0, 否, [[3, 1, 3], [6, 1, 6], [7, 1, 7]], [[1, 3, 3], [1, 6, 6], [1, 7, 7]], 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
12. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,7,4,6],[2,3,5,7,1,6,0,4],[3,5,7,6,2,4,1,0],[4,0,1,2,6,3,7,5],[5,7,6,4,3,0,2,1],[6,4,0,1,7,2,5,3],[7,6,4,0,5,1,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,6,0,5,2],[0,3,6,1,7,5,2,4],[0,4,6,7,1,5,2,3],[0,5,0,5,5,0,0,5],[0,6,5,2,2,0,5,6],[0,7,2,4,3,5,6,1]],"subset":[0,5]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 5], 0, 是, [], [], 是)
Wave4第二層核對=([0, 5], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
13. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,7,4,0],[2,3,6,4,7,0,5,1],[3,6,4,5,0,1,7,2],[4,5,7,0,2,3,1,6],[5,7,0,1,3,6,2,4],[6,4,5,7,1,2,0,3],[7,0,1,2,6,4,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,2,6,0,5],[0,3,5,1,7,2,6,4],[0,4,2,7,1,5,6,3],[0,5,6,2,5,6,0,2],[0,6,0,6,6,0,0,6],[0,7,5,4,3,2,6,1]],"subset":[0]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0], 0, 是, [], [], 是)
Wave4第二層核對=([0], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
14. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,0,4,5],[2,3,6,4,5,1,7,0],[3,6,4,7,0,2,5,1],[4,7,5,0,2,6,1,3],[5,0,1,2,6,7,3,4],[6,4,7,5,1,3,0,2],[7,5,0,1,3,4,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,2,7,0,6],[0,3,7,1,5,4,6,2],[0,4,2,5,1,3,6,7],[0,5,7,4,3,1,6,2],[0,6,0,6,6,6,0,0],[0,7,6,2,7,2,0,6]],"subset":[0,2,6,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 2, 6, 7], 0, 是, [], [], 是)
Wave4第二層核對=([0, 2, 6, 7], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
15. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,4,5,0],[2,3,6,5,0,7,4,1],[3,6,5,4,1,0,7,2],[4,7,0,1,6,3,2,5],[5,4,7,0,3,2,1,6],[6,5,4,7,2,1,0,3],[7,0,1,2,5,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,2,0,4],[0,3,4,1,2,7,6,5],[0,4,6,2,6,4,0,2],[0,5,2,7,4,1,6,3],[0,6,0,6,0,6,0,6],[0,7,4,5,2,3,6,1]],"subset":[0,6]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 6], 0, 是, [], [], 是)
Wave4第二層核對=([0, 6], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
16. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,7,5,4],[2,3,6,5,1,4,7,0],[3,6,5,7,2,0,4,1],[4,0,1,2,7,6,3,5],[5,7,4,0,6,2,1,3],[6,5,7,4,3,1,0,2],[7,4,0,1,5,3,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,7,2,0,6],[0,3,7,1,5,4,6,2],[0,4,7,5,1,3,6,2],[0,5,2,4,3,1,6,7],[0,6,0,6,6,6,0,0],[0,7,6,2,2,7,0,6]],"subset":[0,1,2,6,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 1, 2, 6, 7], 0, 否, [[3, 1, 3], [4, 1, 4], [5, 1, 5]], [[1, 3, 3], [1, 4, 4], [1, 5, 5]], 否)
Wave4第二層核對=([0, 1, 2, 6, 7], 0, 否, [[3, 1, 3], [4, 1, 4], [5, 1, 5]], [[1, 3, 3], [1, 4, 4], [1, 5, 5]], 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
17. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,0,7,4],[2,3,6,7,0,1,4,5],[3,6,7,4,1,2,5,0],[4,5,0,1,6,7,2,3],[5,0,1,2,7,4,3,6],[6,7,4,5,2,3,0,1],[7,4,5,0,3,6,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,4,0,2],[0,3,4,1,2,7,6,5],[0,4,6,2,6,2,0,4],[0,5,4,7,2,1,6,3],[0,6,0,6,0,6,0,6],[0,7,2,5,4,3,6,1]],"subset":[0,6]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 6], 0, 是, [], [], 是)
Wave4第二層核對=([0, 6], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
18. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,4,7,5],[2,3,6,7,1,0,5,4],[3,6,7,5,2,1,4,0],[4,0,1,2,5,7,3,6],[5,4,0,1,7,6,2,3],[6,7,5,4,3,2,0,1],[7,5,4,0,6,3,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,5,6,0,2],[0,3,5,1,7,2,6,4],[0,4,5,7,1,2,6,3],[0,5,6,2,2,6,0,5],[0,6,0,6,6,0,0,6],[0,7,2,4,3,5,6,1]],"subset":[0]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0], 0, 是, [], [], 是)
Wave4第二層核對=([0], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
19. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,6,0,4],[2,3,7,4,6,0,1,5],[3,7,4,5,0,1,2,6],[4,5,6,0,2,3,7,1],[5,6,0,1,3,7,4,2],[6,0,1,2,7,4,5,3],[7,4,5,6,1,2,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,2,7,5,0],[0,3,5,1,6,2,4,7],[0,4,2,6,1,5,3,7],[0,5,7,2,5,7,2,0],[0,6,5,4,3,2,1,7],[0,7,0,7,7,0,7,0]],"subset":[0,2,5,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 2, 5, 7], 0, 是, [], [], 是)
Wave4第二層核對=([0, 2, 5, 7], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
20. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,0,5,4],[2,3,7,4,5,1,0,6],[3,7,4,6,0,2,1,5],[4,6,5,0,2,7,3,1],[5,0,1,2,7,6,4,3],[6,5,0,1,3,4,7,2],[7,4,6,5,1,3,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,2,6,7,0],[0,3,6,1,5,4,2,7],[0,4,2,5,1,3,6,7],[0,5,6,4,3,1,2,7],[0,6,7,2,6,2,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 7], 0, 是, [], [], 是)
Wave4第二層核對=([0, 7], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
21. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,4,0,5],[2,3,7,5,0,6,1,4],[3,7,5,4,1,0,2,6],[4,6,0,1,7,3,5,2],[5,4,6,0,3,2,7,1],[6,0,1,2,5,7,4,3],[7,5,4,6,2,1,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,2,4,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,4,2,0],[0,5,2,6,4,1,3,7],[0,6,4,5,2,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0,1,2,4,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 1, 2, 4, 7], 0, 否, [[3, 1, 3], [5, 1, 5], [6, 1, 6]], [[1, 3, 3], [1, 5, 5], [1, 6, 6]], 否)
Wave4第二層核對=([0, 1, 2, 4, 7], 0, 否, [[3, 1, 3], [5, 1, 5], [6, 1, 6]], [[1, 3, 3], [1, 5, 5], [1, 6, 6]], 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
22. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,6,4,5],[2,3,7,5,1,4,0,6],[3,7,5,6,2,0,1,4],[4,0,1,2,6,7,5,3],[5,6,4,0,7,2,3,1],[6,4,0,1,5,3,7,2],[7,5,6,4,3,1,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,6,2,7,0],[0,3,6,1,5,4,2,7],[0,4,6,5,1,3,2,7],[0,5,2,4,3,1,6,7],[0,6,7,2,2,6,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 7], 0, 是, [], [], 是)
Wave4第二層核對=([0, 7], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
23. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,0,4,6],[2,3,7,6,0,1,5,4],[3,7,6,4,1,2,0,5],[4,5,0,1,7,6,3,2],[5,0,1,2,6,4,7,3],[6,4,5,0,3,7,2,1],[7,6,4,5,2,3,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,4,2,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,2,4,0],[0,5,4,6,2,1,3,7],[0,6,2,5,4,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0], 0, 是, [], [], 是)
Wave4第二層核對=([0], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
24. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,4,5,6],[2,3,7,6,1,0,4,5],[3,7,6,5,2,1,0,4],[4,0,1,2,5,6,7,3],[5,4,0,1,6,7,3,2],[6,5,4,0,7,3,2,1],[7,6,5,4,3,2,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,5,7,2,0],[0,3,5,1,6,2,4,7],[0,4,5,6,1,2,3,7],[0,5,7,2,2,7,5,0],[0,6,2,4,3,5,1,7],[0,7,0,7,7,0,7,0]],"subset":[0,2,5,7]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 2, 5, 7], 0, 是, [], [], 是)
Wave4第二層核對=([0, 2, 5, 7], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
25. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,4,5,3,6,7,0],[2,4,3,6,5,7,0,1],[3,5,6,0,7,1,2,4],[4,3,5,7,6,0,1,2],[5,6,7,1,0,2,4,3],[6,7,0,2,1,4,3,5],[7,0,1,4,2,3,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,3,0,6,2,3,6],[0,3,0,0,3,3,0,3],[0,4,6,3,1,7,2,5],[0,5,2,3,7,1,6,4],[0,6,3,0,2,6,3,2],[0,7,6,3,5,4,2,1]],"subset":[0,3]}。請依 [subset,zero,additive_subgroup,missing_left,missing_right,two_sided_ideal] 欄序回答。
查看答案與解釋
([0, 3], 0, 是, [], [], 是)
Wave4第二層核對=([0, 3], 0, 是, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-qualification · candidate
26. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,2,4,6],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,2,7,4,1,6,3],[0,6,4,2,0,6,4,2],[0,7,6,5,4,3,2,1]],"subset":[0,2,4,6]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 4, 6], 0, [], [], 是)
Wave4第二層核對=([0, 2, 4, 6], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
27. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,7,0,6],[2,3,4,5,7,6,1,0],[3,4,5,7,6,0,2,1],[4,5,7,6,0,1,3,2],[5,7,6,0,1,2,4,3],[6,0,1,2,3,4,7,5],[7,6,0,1,2,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,2,7,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,2,6,4,1,3,7],[0,6,7,5,4,3,1,2],[0,7,4,2,0,7,2,4]],"subset":[0,4]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 4], 0, [], [], 是)
Wave4第二層核對=([0, 4], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
28. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,7,5,0],[2,3,4,6,5,0,7,1],[3,4,6,5,7,1,0,2],[4,6,5,7,0,2,1,3],[5,7,0,1,2,4,3,6],[6,5,7,0,1,3,2,4],[7,0,1,2,3,6,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,2,5],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,5,2],[0,6,2,7,4,5,1,3],[0,7,5,6,4,2,3,1]],"subset":[0]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0], 0, [], [], 是)
Wave4第二層核對=([0], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
29. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,0,7,5],[2,3,4,6,7,1,5,0],[3,4,6,7,5,2,0,1],[4,6,7,5,0,3,1,2],[5,0,1,2,3,7,4,6],[6,7,5,0,1,4,2,3],[7,5,0,1,2,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,7,2,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,7,6,4,1,3,2],[0,6,2,5,4,3,1,7],[0,7,4,2,0,2,7,4]],"subset":[0,2,4,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 4, 7], 0, [], [], 是)
Wave4第二層核對=([0, 2, 4, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
30. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,6,0,5],[2,3,4,7,5,0,1,6],[3,4,7,5,6,1,2,0],[4,7,5,6,0,2,3,1],[5,6,0,1,2,4,7,3],[6,0,1,2,3,7,5,4],[7,5,6,0,1,3,4,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,5,2],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,2,5],[0,6,5,7,4,2,1,3],[0,7,2,6,4,5,3,1]],"subset":[0,4]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 4], 0, [], [], 是)
Wave4第二層核對=([0, 4], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
31. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,0,5,6],[2,3,4,7,6,1,0,5],[3,4,7,6,5,2,1,0],[4,7,6,5,0,3,2,1],[5,0,1,2,3,6,7,4],[6,5,0,1,2,7,4,3],[7,6,5,0,1,4,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,6,4,2],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,6,7,4,1,2,3],[0,6,4,2,0,2,4,6],[0,7,2,5,4,3,6,1]],"subset":[0,2,4,6]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 4, 6], 0, [], [], 是)
Wave4第二層核對=([0, 2, 4, 6], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
32. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,4,7,0],[2,3,5,4,7,6,0,1],[3,5,4,6,0,7,1,2],[4,6,7,0,2,1,3,5],[5,4,6,7,1,0,2,3],[6,7,0,1,3,2,5,4],[7,0,1,2,5,3,4,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,2,0,5,6],[0,3,6,1,7,5,2,4],[0,4,2,7,1,5,6,3],[0,5,0,5,5,0,0,5],[0,6,5,2,6,0,5,2],[0,7,6,4,3,5,2,1]],"subset":[0,5]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 5], 0, [], [], 是)
Wave4第二層核對=([0, 5], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
33. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,4,0,6],[2,3,5,4,6,7,1,0],[3,5,4,7,0,6,2,1],[4,7,6,0,2,1,5,3],[5,4,7,6,1,0,3,2],[6,0,1,2,5,3,7,4],[7,6,0,1,3,2,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,2,0,7,5],[0,3,7,1,6,5,4,2],[0,4,2,6,1,5,3,7],[0,5,0,5,5,0,5,0],[0,6,7,4,3,5,1,2],[0,7,5,2,7,0,2,5]],"subset":[0]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0], 0, [], [], 是)
Wave4第二層核對=([0], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
34. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,6,4,0],[2,3,5,6,0,4,7,1],[3,5,6,4,1,7,0,2],[4,7,0,1,5,2,3,6],[5,6,4,7,2,0,1,3],[6,4,7,0,3,1,2,5],[7,0,1,2,6,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,2,4],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,4,2],[0,5,0,5,0,0,5,5],[0,6,2,7,4,5,1,3],[0,7,4,6,2,5,3,1]],"subset":[0,2,4,5]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 4, 5], 0, [], [], 是)
Wave4第二層核對=([0, 2, 4, 5], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
35. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,6,7,4],[2,3,5,6,1,7,4,0],[3,5,6,7,2,4,0,1],[4,0,1,2,7,3,5,6],[5,6,7,4,3,0,1,2],[6,7,4,0,5,1,2,3],[7,4,0,1,6,2,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,7,0,2,5],[0,3,7,1,6,5,4,2],[0,4,7,6,1,5,3,2],[0,5,0,5,5,0,5,0],[0,6,2,4,3,5,1,7],[0,7,5,2,2,0,7,5]],"subset":[0,5]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 5], 0, [], [], 是)
Wave4第二層核對=([0, 5], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
36. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,7,0,4],[2,3,5,7,0,4,1,6],[3,5,7,4,1,6,2,0],[4,6,0,1,5,2,7,3],[5,7,4,6,2,0,3,1],[6,0,1,2,7,3,4,5],[7,4,6,0,3,1,5,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,4,2],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,2,4],[0,5,0,5,0,0,5,5],[0,6,4,7,2,5,1,3],[0,7,2,6,4,5,3,1]],"subset":[0,2,4,5]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 4, 5], 0, [], [], 是)
Wave4第二層核對=([0, 2, 4, 5], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
37. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,7,4,6],[2,3,5,7,1,6,0,4],[3,5,7,6,2,4,1,0],[4,0,1,2,6,3,7,5],[5,7,6,4,3,0,2,1],[6,4,0,1,7,2,5,3],[7,6,4,0,5,1,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,6,0,5,2],[0,3,6,1,7,5,2,4],[0,4,6,7,1,5,2,3],[0,5,0,5,5,0,0,5],[0,6,5,2,2,0,5,6],[0,7,2,4,3,5,6,1]],"subset":[0,5]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 5], 0, [], [], 是)
Wave4第二層核對=([0, 5], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
38. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,7,4,0],[2,3,6,4,7,0,5,1],[3,6,4,5,0,1,7,2],[4,5,7,0,2,3,1,6],[5,7,0,1,3,6,2,4],[6,4,5,7,1,2,0,3],[7,0,1,2,6,4,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,2,6,0,5],[0,3,5,1,7,2,6,4],[0,4,2,7,1,5,6,3],[0,5,6,2,5,6,0,2],[0,6,0,6,6,0,0,6],[0,7,5,4,3,2,6,1]],"subset":[0]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0], 0, [], [], 是)
Wave4第二層核對=([0], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
39. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,0,4,5],[2,3,6,4,5,1,7,0],[3,6,4,7,0,2,5,1],[4,7,5,0,2,6,1,3],[5,0,1,2,6,7,3,4],[6,4,7,5,1,3,0,2],[7,5,0,1,3,4,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,2,7,0,6],[0,3,7,1,5,4,6,2],[0,4,2,5,1,3,6,7],[0,5,7,4,3,1,6,2],[0,6,0,6,6,6,0,0],[0,7,6,2,7,2,0,6]],"subset":[0,2,6,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 6, 7], 0, [], [], 是)
Wave4第二層核對=([0, 2, 6, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
40. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,4,5,0],[2,3,6,5,0,7,4,1],[3,6,5,4,1,0,7,2],[4,7,0,1,6,3,2,5],[5,4,7,0,3,2,1,6],[6,5,4,7,2,1,0,3],[7,0,1,2,5,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,2,0,4],[0,3,4,1,2,7,6,5],[0,4,6,2,6,4,0,2],[0,5,2,7,4,1,6,3],[0,6,0,6,0,6,0,6],[0,7,4,5,2,3,6,1]],"subset":[0,6]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 6], 0, [], [], 是)
Wave4第二層核對=([0, 6], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
41. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,7,5,4],[2,3,6,5,1,4,7,0],[3,6,5,7,2,0,4,1],[4,0,1,2,7,6,3,5],[5,7,4,0,6,2,1,3],[6,5,7,4,3,1,0,2],[7,4,0,1,5,3,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,7,2,0,6],[0,3,7,1,5,4,6,2],[0,4,7,5,1,3,6,2],[0,5,2,4,3,1,6,7],[0,6,0,6,6,6,0,0],[0,7,6,2,2,7,0,6]],"subset":[0,2,6,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 6, 7], 0, [], [], 是)
Wave4第二層核對=([0, 2, 6, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
42. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,0,7,4],[2,3,6,7,0,1,4,5],[3,6,7,4,1,2,5,0],[4,5,0,1,6,7,2,3],[5,0,1,2,7,4,3,6],[6,7,4,5,2,3,0,1],[7,4,5,0,3,6,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,4,0,2],[0,3,4,1,2,7,6,5],[0,4,6,2,6,2,0,4],[0,5,4,7,2,1,6,3],[0,6,0,6,0,6,0,6],[0,7,2,5,4,3,6,1]],"subset":[0,6]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 6], 0, [], [], 是)
Wave4第二層核對=([0, 6], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
43. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,4,7,5],[2,3,6,7,1,0,5,4],[3,6,7,5,2,1,4,0],[4,0,1,2,5,7,3,6],[5,4,0,1,7,6,2,3],[6,7,5,4,3,2,0,1],[7,5,4,0,6,3,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,5,6,0,2],[0,3,5,1,7,2,6,4],[0,4,5,7,1,2,6,3],[0,5,6,2,2,6,0,5],[0,6,0,6,6,0,0,6],[0,7,2,4,3,5,6,1]],"subset":[0]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0], 0, [], [], 是)
Wave4第二層核對=([0], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
44. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,6,0,4],[2,3,7,4,6,0,1,5],[3,7,4,5,0,1,2,6],[4,5,6,0,2,3,7,1],[5,6,0,1,3,7,4,2],[6,0,1,2,7,4,5,3],[7,4,5,6,1,2,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,2,7,5,0],[0,3,5,1,6,2,4,7],[0,4,2,6,1,5,3,7],[0,5,7,2,5,7,2,0],[0,6,5,4,3,2,1,7],[0,7,0,7,7,0,7,0]],"subset":[0,2,5,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 5, 7], 0, [], [], 是)
Wave4第二層核對=([0, 2, 5, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
45. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,0,5,4],[2,3,7,4,5,1,0,6],[3,7,4,6,0,2,1,5],[4,6,5,0,2,7,3,1],[5,0,1,2,7,6,4,3],[6,5,0,1,3,4,7,2],[7,4,6,5,1,3,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,2,6,7,0],[0,3,6,1,5,4,2,7],[0,4,2,5,1,3,6,7],[0,5,6,4,3,1,2,7],[0,6,7,2,6,2,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 7], 0, [], [], 是)
Wave4第二層核對=([0, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
46. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,4,0,5],[2,3,7,5,0,6,1,4],[3,7,5,4,1,0,2,6],[4,6,0,1,7,3,5,2],[5,4,6,0,3,2,7,1],[6,0,1,2,5,7,4,3],[7,5,4,6,2,1,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,2,4,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,4,2,0],[0,5,2,6,4,1,3,7],[0,6,4,5,2,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0,2,4,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 4, 7], 0, [], [], 是)
Wave4第二層核對=([0, 2, 4, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
47. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,6,4,5],[2,3,7,5,1,4,0,6],[3,7,5,6,2,0,1,4],[4,0,1,2,6,7,5,3],[5,6,4,0,7,2,3,1],[6,4,0,1,5,3,7,2],[7,5,6,4,3,1,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,6,2,7,0],[0,3,6,1,5,4,2,7],[0,4,6,5,1,3,2,7],[0,5,2,4,3,1,6,7],[0,6,7,2,2,6,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 7], 0, [], [], 是)
Wave4第二層核對=([0, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
48. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,0,4,6],[2,3,7,6,0,1,5,4],[3,7,6,4,1,2,0,5],[4,5,0,1,7,6,3,2],[5,0,1,2,6,4,7,3],[6,4,5,0,3,7,2,1],[7,6,4,5,2,3,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,4,2,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,2,4,0],[0,5,4,6,2,1,3,7],[0,6,2,5,4,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0], 0, [], [], 是)
Wave4第二層核對=([0], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
49. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,4,5,6],[2,3,7,6,1,0,4,5],[3,7,6,5,2,1,0,4],[4,0,1,2,5,6,7,3],[5,4,0,1,6,7,3,2],[6,5,4,0,7,3,2,1],[7,6,5,4,3,2,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,5,7,2,0],[0,3,5,1,6,2,4,7],[0,4,5,6,1,2,3,7],[0,5,7,2,2,7,5,0],[0,6,2,4,3,5,1,7],[0,7,0,7,7,0,7,0]],"subset":[0,2,5,7]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 2, 5, 7], 0, [], [], 是)
Wave4第二層核對=([0, 2, 5, 7], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
50. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-additive-subgroup；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,4,5,3,6,7,0],[2,4,3,6,5,7,0,1],[3,5,6,0,7,1,2,4],[4,3,5,7,6,0,1,2],[5,6,7,1,0,2,4,3],[6,7,0,2,1,4,3,5],[7,0,1,4,2,3,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,3,0,6,2,3,6],[0,3,0,0,3,3,0,3],[0,4,6,3,1,7,2,5],[0,5,2,3,7,1,6,4],[0,6,3,0,2,6,3,2],[0,7,6,3,5,4,2,1]],"subset":[0,3]}。請依 [subset,zero,missing_additions,missing_inverses,additive_subgroup] 欄序回答。
查看答案與解釋
([0, 3], 0, [], [], 是)
Wave4第二層核對=([0, 3], 0, [], [], 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-additive-subgroup · candidate
51. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,2,4,6],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,2,7,4,1,6,3],[0,6,4,2,0,6,4,2],[0,7,6,5,4,3,2,1]],"subset":[0,2,4,6]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 4, 6], [], [], 是, 是)
Wave4第二層核對=([0, 2, 4, 6], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
52. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,7,0,6],[2,3,4,5,7,6,1,0],[3,4,5,7,6,0,2,1],[4,5,7,6,0,1,3,2],[5,7,6,0,1,2,4,3],[6,0,1,2,3,4,7,5],[7,6,0,1,2,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,2,7,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,2,6,4,1,3,7],[0,6,7,5,4,3,1,2],[0,7,4,2,0,7,2,4]],"subset":[0,4]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 4], [], [], 是, 是)
Wave4第二層核對=([0, 4], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
53. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,7,5,0],[2,3,4,6,5,0,7,1],[3,4,6,5,7,1,0,2],[4,6,5,7,0,2,1,3],[5,7,0,1,2,4,3,6],[6,5,7,0,1,3,2,4],[7,0,1,2,3,6,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,2,5],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,5,2],[0,6,2,7,4,5,1,3],[0,7,5,6,4,2,3,1]],"subset":[0]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0], [], [], 是, 是)
Wave4第二層核對=([0], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
54. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,0,7,5],[2,3,4,6,7,1,5,0],[3,4,6,7,5,2,0,1],[4,6,7,5,0,3,1,2],[5,0,1,2,3,7,4,6],[6,7,5,0,1,4,2,3],[7,5,0,1,2,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,7,2,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,7,6,4,1,3,2],[0,6,2,5,4,3,1,7],[0,7,4,2,0,2,7,4]],"subset":[0,2,4,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 4, 7], [], [], 是, 是)
Wave4第二層核對=([0, 2, 4, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
55. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,6,0,5],[2,3,4,7,5,0,1,6],[3,4,7,5,6,1,2,0],[4,7,5,6,0,2,3,1],[5,6,0,1,2,4,7,3],[6,0,1,2,3,7,5,4],[7,5,6,0,1,3,4,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,5,2],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,2,5],[0,6,5,7,4,2,1,3],[0,7,2,6,4,5,3,1]],"subset":[0,4]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 4], [], [], 是, 是)
Wave4第二層核對=([0, 4], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
56. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,0,5,6],[2,3,4,7,6,1,0,5],[3,4,7,6,5,2,1,0],[4,7,6,5,0,3,2,1],[5,0,1,2,3,6,7,4],[6,5,0,1,2,7,4,3],[7,6,5,0,1,4,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,6,4,2],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,6,7,4,1,2,3],[0,6,4,2,0,2,4,6],[0,7,2,5,4,3,6,1]],"subset":[0,2,4,6]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 4, 6], [], [], 是, 是)
Wave4第二層核對=([0, 2, 4, 6], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
57. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,4,7,0],[2,3,5,4,7,6,0,1],[3,5,4,6,0,7,1,2],[4,6,7,0,2,1,3,5],[5,4,6,7,1,0,2,3],[6,7,0,1,3,2,5,4],[7,0,1,2,5,3,4,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,2,0,5,6],[0,3,6,1,7,5,2,4],[0,4,2,7,1,5,6,3],[0,5,0,5,5,0,0,5],[0,6,5,2,6,0,5,2],[0,7,6,4,3,5,2,1]],"subset":[0,5]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 5], [], [], 是, 是)
Wave4第二層核對=([0, 5], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
58. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,4,0,6],[2,3,5,4,6,7,1,0],[3,5,4,7,0,6,2,1],[4,7,6,0,2,1,5,3],[5,4,7,6,1,0,3,2],[6,0,1,2,5,3,7,4],[7,6,0,1,3,2,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,2,0,7,5],[0,3,7,1,6,5,4,2],[0,4,2,6,1,5,3,7],[0,5,0,5,5,0,5,0],[0,6,7,4,3,5,1,2],[0,7,5,2,7,0,2,5]],"subset":[0]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0], [], [], 是, 是)
Wave4第二層核對=([0], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
59. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,6,4,0],[2,3,5,6,0,4,7,1],[3,5,6,4,1,7,0,2],[4,7,0,1,5,2,3,6],[5,6,4,7,2,0,1,3],[6,4,7,0,3,1,2,5],[7,0,1,2,6,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,2,4],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,4,2],[0,5,0,5,0,0,5,5],[0,6,2,7,4,5,1,3],[0,7,4,6,2,5,3,1]],"subset":[0,2,4,5]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 4, 5], [], [], 是, 是)
Wave4第二層核對=([0, 2, 4, 5], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
60. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,6,7,4],[2,3,5,6,1,7,4,0],[3,5,6,7,2,4,0,1],[4,0,1,2,7,3,5,6],[5,6,7,4,3,0,1,2],[6,7,4,0,5,1,2,3],[7,4,0,1,6,2,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,7,0,2,5],[0,3,7,1,6,5,4,2],[0,4,7,6,1,5,3,2],[0,5,0,5,5,0,5,0],[0,6,2,4,3,5,1,7],[0,7,5,2,2,0,7,5]],"subset":[0,5]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 5], [], [], 是, 是)
Wave4第二層核對=([0, 5], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
61. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,7,0,4],[2,3,5,7,0,4,1,6],[3,5,7,4,1,6,2,0],[4,6,0,1,5,2,7,3],[5,7,4,6,2,0,3,1],[6,0,1,2,7,3,4,5],[7,4,6,0,3,1,5,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,4,2],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,2,4],[0,5,0,5,0,0,5,5],[0,6,4,7,2,5,1,3],[0,7,2,6,4,5,3,1]],"subset":[0,2,4,5]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 4, 5], [], [], 是, 是)
Wave4第二層核對=([0, 2, 4, 5], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
62. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,7,4,6],[2,3,5,7,1,6,0,4],[3,5,7,6,2,4,1,0],[4,0,1,2,6,3,7,5],[5,7,6,4,3,0,2,1],[6,4,0,1,7,2,5,3],[7,6,4,0,5,1,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,6,0,5,2],[0,3,6,1,7,5,2,4],[0,4,6,7,1,5,2,3],[0,5,0,5,5,0,0,5],[0,6,5,2,2,0,5,6],[0,7,2,4,3,5,6,1]],"subset":[0,5]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 5], [], [], 是, 是)
Wave4第二層核對=([0, 5], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
63. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,7,4,0],[2,3,6,4,7,0,5,1],[3,6,4,5,0,1,7,2],[4,5,7,0,2,3,1,6],[5,7,0,1,3,6,2,4],[6,4,5,7,1,2,0,3],[7,0,1,2,6,4,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,2,6,0,5],[0,3,5,1,7,2,6,4],[0,4,2,7,1,5,6,3],[0,5,6,2,5,6,0,2],[0,6,0,6,6,0,0,6],[0,7,5,4,3,2,6,1]],"subset":[0]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0], [], [], 是, 是)
Wave4第二層核對=([0], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
64. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,0,4,5],[2,3,6,4,5,1,7,0],[3,6,4,7,0,2,5,1],[4,7,5,0,2,6,1,3],[5,0,1,2,6,7,3,4],[6,4,7,5,1,3,0,2],[7,5,0,1,3,4,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,2,7,0,6],[0,3,7,1,5,4,6,2],[0,4,2,5,1,3,6,7],[0,5,7,4,3,1,6,2],[0,6,0,6,6,6,0,0],[0,7,6,2,7,2,0,6]],"subset":[0,2,6,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 6, 7], [], [], 是, 是)
Wave4第二層核對=([0, 2, 6, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
65. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,4,5,0],[2,3,6,5,0,7,4,1],[3,6,5,4,1,0,7,2],[4,7,0,1,6,3,2,5],[5,4,7,0,3,2,1,6],[6,5,4,7,2,1,0,3],[7,0,1,2,5,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,2,0,4],[0,3,4,1,2,7,6,5],[0,4,6,2,6,4,0,2],[0,5,2,7,4,1,6,3],[0,6,0,6,0,6,0,6],[0,7,4,5,2,3,6,1]],"subset":[0,6]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 6], [], [], 是, 是)
Wave4第二層核對=([0, 6], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
66. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,7,5,4],[2,3,6,5,1,4,7,0],[3,6,5,7,2,0,4,1],[4,0,1,2,7,6,3,5],[5,7,4,0,6,2,1,3],[6,5,7,4,3,1,0,2],[7,4,0,1,5,3,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,7,2,0,6],[0,3,7,1,5,4,6,2],[0,4,7,5,1,3,6,2],[0,5,2,4,3,1,6,7],[0,6,0,6,6,6,0,0],[0,7,6,2,2,7,0,6]],"subset":[0,2,6,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 6, 7], [], [], 是, 是)
Wave4第二層核對=([0, 2, 6, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
67. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,0,7,4],[2,3,6,7,0,1,4,5],[3,6,7,4,1,2,5,0],[4,5,0,1,6,7,2,3],[5,0,1,2,7,4,3,6],[6,7,4,5,2,3,0,1],[7,4,5,0,3,6,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,4,0,2],[0,3,4,1,2,7,6,5],[0,4,6,2,6,2,0,4],[0,5,4,7,2,1,6,3],[0,6,0,6,0,6,0,6],[0,7,2,5,4,3,6,1]],"subset":[0,6]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 6], [], [], 是, 是)
Wave4第二層核對=([0, 6], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
68. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,4,7,5],[2,3,6,7,1,0,5,4],[3,6,7,5,2,1,4,0],[4,0,1,2,5,7,3,6],[5,4,0,1,7,6,2,3],[6,7,5,4,3,2,0,1],[7,5,4,0,6,3,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,5,6,0,2],[0,3,5,1,7,2,6,4],[0,4,5,7,1,2,6,3],[0,5,6,2,2,6,0,5],[0,6,0,6,6,0,0,6],[0,7,2,4,3,5,6,1]],"subset":[0]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0], [], [], 是, 是)
Wave4第二層核對=([0], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
69. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,6,0,4],[2,3,7,4,6,0,1,5],[3,7,4,5,0,1,2,6],[4,5,6,0,2,3,7,1],[5,6,0,1,3,7,4,2],[6,0,1,2,7,4,5,3],[7,4,5,6,1,2,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,2,7,5,0],[0,3,5,1,6,2,4,7],[0,4,2,6,1,5,3,7],[0,5,7,2,5,7,2,0],[0,6,5,4,3,2,1,7],[0,7,0,7,7,0,7,0]],"subset":[0,2,5,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 5, 7], [], [], 是, 是)
Wave4第二層核對=([0, 2, 5, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
70. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,0,5,4],[2,3,7,4,5,1,0,6],[3,7,4,6,0,2,1,5],[4,6,5,0,2,7,3,1],[5,0,1,2,7,6,4,3],[6,5,0,1,3,4,7,2],[7,4,6,5,1,3,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,2,6,7,0],[0,3,6,1,5,4,2,7],[0,4,2,5,1,3,6,7],[0,5,6,4,3,1,2,7],[0,6,7,2,6,2,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 7], [], [], 是, 是)
Wave4第二層核對=([0, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
71. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,4,0,5],[2,3,7,5,0,6,1,4],[3,7,5,4,1,0,2,6],[4,6,0,1,7,3,5,2],[5,4,6,0,3,2,7,1],[6,0,1,2,5,7,4,3],[7,5,4,6,2,1,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,2,4,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,4,2,0],[0,5,2,6,4,1,3,7],[0,6,4,5,2,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0,2,4,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 4, 7], [], [], 是, 是)
Wave4第二層核對=([0, 2, 4, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
72. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,6,4,5],[2,3,7,5,1,4,0,6],[3,7,5,6,2,0,1,4],[4,0,1,2,6,7,5,3],[5,6,4,0,7,2,3,1],[6,4,0,1,5,3,7,2],[7,5,6,4,3,1,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,6,2,7,0],[0,3,6,1,5,4,2,7],[0,4,6,5,1,3,2,7],[0,5,2,4,3,1,6,7],[0,6,7,2,2,6,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 7], [], [], 是, 是)
Wave4第二層核對=([0, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
73. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,0,4,6],[2,3,7,6,0,1,5,4],[3,7,6,4,1,2,0,5],[4,5,0,1,7,6,3,2],[5,0,1,2,6,4,7,3],[6,4,5,0,3,7,2,1],[7,6,4,5,2,3,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,4,2,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,2,4,0],[0,5,4,6,2,1,3,7],[0,6,2,5,4,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0], [], [], 是, 是)
Wave4第二層核對=([0], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
74. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,4,5,6],[2,3,7,6,1,0,4,5],[3,7,6,5,2,1,0,4],[4,0,1,2,5,6,7,3],[5,4,0,1,6,7,3,2],[6,5,4,0,7,3,2,1],[7,6,5,4,3,2,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,5,7,2,0],[0,3,5,1,6,2,4,7],[0,4,5,6,1,2,3,7],[0,5,7,2,2,7,5,0],[0,6,2,4,3,5,1,7],[0,7,0,7,7,0,7,0]],"subset":[0,2,5,7]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 2, 5, 7], [], [], 是, 是)
Wave4第二層核對=([0, 2, 5, 7], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
75. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-two-sided-absorption；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,4,5,3,6,7,0],[2,4,3,6,5,7,0,1],[3,5,6,0,7,1,2,4],[4,3,5,7,6,0,1,2],[5,6,7,1,0,2,4,3],[6,7,0,2,1,4,3,5],[7,0,1,4,2,3,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,3,0,6,2,3,6],[0,3,0,0,3,3,0,3],[0,4,6,3,1,7,2,5],[0,5,2,3,7,1,6,4],[0,6,3,0,2,6,3,2],[0,7,6,3,5,4,2,1]],"subset":[0,3]}。請依 [subset,missing_left,missing_right,left_absorbing,right_absorbing] 欄序回答。
查看答案與解釋
([0, 3], [], [], 是, 是)
Wave4第二層核對=([0, 3], [], [], 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-two-sided-absorption · candidate
76. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,2,4,6],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,2,7,4,1,6,3],[0,6,4,2,0,6,4,2],[0,7,6,5,4,3,2,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
77. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,7,0,6],[2,3,4,5,7,6,1,0],[3,4,5,7,6,0,2,1],[4,5,7,6,0,1,3,2],[5,7,6,0,1,2,4,3],[6,0,1,2,3,4,7,5],[7,6,0,1,2,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,2,7,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,2,6,4,1,3,7],[0,6,7,5,4,3,1,2],[0,7,4,2,0,7,2,4]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
78. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,7,5,0],[2,3,4,6,5,0,7,1],[3,4,6,5,7,1,0,2],[4,6,5,7,0,2,1,3],[5,7,0,1,2,4,3,6],[6,5,7,0,1,3,2,4],[7,0,1,2,3,6,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,2,5],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,5,2],[0,6,2,7,4,5,1,3],[0,7,5,6,4,2,3,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
79. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,6,0,7,5],[2,3,4,6,7,1,5,0],[3,4,6,7,5,2,0,1],[4,6,7,5,0,3,1,2],[5,0,1,2,3,7,4,6],[6,7,5,0,1,4,2,3],[7,5,0,1,2,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,7,0,7,2,4],[0,3,7,1,4,6,5,2],[0,4,0,4,0,4,4,0],[0,5,7,6,4,1,3,2],[0,6,2,5,4,3,1,7],[0,7,4,2,0,2,7,4]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
80. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,6,0,5],[2,3,4,7,5,0,1,6],[3,4,7,5,6,1,2,0],[4,7,5,6,0,2,3,1],[5,6,0,1,2,4,7,3],[6,0,1,2,3,7,5,4],[7,5,6,0,1,3,4,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,5,0,4,5,2],[0,3,5,1,4,2,7,6],[0,4,0,4,0,0,4,4],[0,5,4,2,0,4,2,5],[0,6,5,7,4,2,1,3],[0,7,2,6,4,5,3,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
81. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,4,7,0,5,6],[2,3,4,7,6,1,0,5],[3,4,7,6,5,2,1,0],[4,7,6,5,0,3,2,1],[5,0,1,2,3,6,7,4],[6,5,0,1,2,7,4,3],[7,6,5,0,1,4,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,4,6,0,6,4,2],[0,3,6,1,4,7,2,5],[0,4,0,4,0,4,0,4],[0,5,6,7,4,1,2,3],[0,6,4,2,0,2,4,6],[0,7,2,5,4,3,6,1]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
82. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,4,7,0],[2,3,5,4,7,6,0,1],[3,5,4,6,0,7,1,2],[4,6,7,0,2,1,3,5],[5,4,6,7,1,0,2,3],[6,7,0,1,3,2,5,4],[7,0,1,2,5,3,4,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,2,0,5,6],[0,3,6,1,7,5,2,4],[0,4,2,7,1,5,6,3],[0,5,0,5,5,0,0,5],[0,6,5,2,6,0,5,2],[0,7,6,4,3,5,2,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
83. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,4,0,6],[2,3,5,4,6,7,1,0],[3,5,4,7,0,6,2,1],[4,7,6,0,2,1,5,3],[5,4,7,6,1,0,3,2],[6,0,1,2,5,3,7,4],[7,6,0,1,3,2,4,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,2,0,7,5],[0,3,7,1,6,5,4,2],[0,4,2,6,1,5,3,7],[0,5,0,5,5,0,5,0],[0,6,7,4,3,5,1,2],[0,7,5,2,7,0,2,5]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
84. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,7,6,4,0],[2,3,5,6,0,4,7,1],[3,5,6,4,1,7,0,2],[4,7,0,1,5,2,3,6],[5,6,4,7,2,0,1,3],[6,4,7,0,3,1,2,5],[7,0,1,2,6,3,5,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,2,4],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,4,2],[0,5,0,5,0,0,5,5],[0,6,2,7,4,5,1,3],[0,7,4,6,2,5,3,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
85. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,6,7,4],[2,3,5,6,1,7,4,0],[3,5,6,7,2,4,0,1],[4,0,1,2,7,3,5,6],[5,6,7,4,3,0,1,2],[6,7,4,0,5,1,2,3],[7,4,0,1,6,2,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,7,7,0,2,5],[0,3,7,1,6,5,4,2],[0,4,7,6,1,5,3,2],[0,5,0,5,5,0,5,0],[0,6,2,4,3,5,1,7],[0,7,5,2,2,0,7,5]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
86. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,6,7,0,4],[2,3,5,7,0,4,1,6],[3,5,7,4,1,6,2,0],[4,6,0,1,5,2,7,3],[5,7,4,6,2,0,3,1],[6,0,1,2,7,3,4,5],[7,4,6,0,3,1,5,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,4,5,0,4,2],[0,3,4,1,2,5,7,6],[0,4,5,2,5,0,2,4],[0,5,0,5,0,0,5,5],[0,6,4,7,2,5,1,3],[0,7,2,6,4,5,3,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
87. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,5,0,7,4,6],[2,3,5,7,1,6,0,4],[3,5,7,6,2,4,1,0],[4,0,1,2,6,3,7,5],[5,7,6,4,3,0,2,1],[6,4,0,1,7,2,5,3],[7,6,4,0,5,1,3,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,5,6,6,0,5,2],[0,3,6,1,7,5,2,4],[0,4,6,7,1,5,2,3],[0,5,0,5,5,0,0,5],[0,6,5,2,2,0,5,6],[0,7,2,4,3,5,6,1]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
88. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,7,4,0],[2,3,6,4,7,0,5,1],[3,6,4,5,0,1,7,2],[4,5,7,0,2,3,1,6],[5,7,0,1,3,6,2,4],[6,4,5,7,1,2,0,3],[7,0,1,2,6,4,3,5]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,2,6,0,5],[0,3,5,1,7,2,6,4],[0,4,2,7,1,5,6,3],[0,5,6,2,5,6,0,2],[0,6,0,6,6,0,0,6],[0,7,5,4,3,2,6,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
89. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,0,4,5],[2,3,6,4,5,1,7,0],[3,6,4,7,0,2,5,1],[4,7,5,0,2,6,1,3],[5,0,1,2,6,7,3,4],[6,4,7,5,1,3,0,2],[7,5,0,1,3,4,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,2,7,0,6],[0,3,7,1,5,4,6,2],[0,4,2,5,1,3,6,7],[0,5,7,4,3,1,6,2],[0,6,0,6,6,6,0,0],[0,7,6,2,7,2,0,6]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
90. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,7,4,5,0],[2,3,6,5,0,7,4,1],[3,6,5,4,1,0,7,2],[4,7,0,1,6,3,2,5],[5,4,7,0,3,2,1,6],[6,5,4,7,2,1,0,3],[7,0,1,2,5,6,3,4]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,2,0,4],[0,3,4,1,2,7,6,5],[0,4,6,2,6,4,0,2],[0,5,2,7,4,1,6,3],[0,6,0,6,0,6,0,6],[0,7,4,5,2,3,6,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
91. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,7,5,4],[2,3,6,5,1,4,7,0],[3,6,5,7,2,0,4,1],[4,0,1,2,7,6,3,5],[5,7,4,0,6,2,1,3],[6,5,7,4,3,1,0,2],[7,4,0,1,5,3,2,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,7,7,2,0,6],[0,3,7,1,5,4,6,2],[0,4,7,5,1,3,6,2],[0,5,2,4,3,1,6,7],[0,6,0,6,6,6,0,0],[0,7,6,2,2,7,0,6]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
92. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,5,0,7,4],[2,3,6,7,0,1,4,5],[3,6,7,4,1,2,5,0],[4,5,0,1,6,7,2,3],[5,0,1,2,7,4,3,6],[6,7,4,5,2,3,0,1],[7,4,5,0,3,6,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,4,6,4,0,2],[0,3,4,1,2,7,6,5],[0,4,6,2,6,2,0,4],[0,5,4,7,2,1,6,3],[0,6,0,6,0,6,0,6],[0,7,2,5,4,3,6,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
93. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,6,0,4,7,5],[2,3,6,7,1,0,5,4],[3,6,7,5,2,1,4,0],[4,0,1,2,5,7,3,6],[5,4,0,1,7,6,2,3],[6,7,5,4,3,2,0,1],[7,5,4,0,6,3,1,2]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,6,5,5,6,0,2],[0,3,5,1,7,2,6,4],[0,4,5,7,1,2,6,3],[0,5,6,2,2,6,0,5],[0,6,0,6,6,0,0,6],[0,7,2,4,3,5,6,1]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
94. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,6,0,4],[2,3,7,4,6,0,1,5],[3,7,4,5,0,1,2,6],[4,5,6,0,2,3,7,1],[5,6,0,1,3,7,4,2],[6,0,1,2,7,4,5,3],[7,4,5,6,1,2,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,2,7,5,0],[0,3,5,1,6,2,4,7],[0,4,2,6,1,5,3,7],[0,5,7,2,5,7,2,0],[0,6,5,4,3,2,1,7],[0,7,0,7,7,0,7,0]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
95. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,0,5,4],[2,3,7,4,5,1,0,6],[3,7,4,6,0,2,1,5],[4,6,5,0,2,7,3,1],[5,0,1,2,7,6,4,3],[6,5,0,1,3,4,7,2],[7,4,6,5,1,3,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,2,6,7,0],[0,3,6,1,5,4,2,7],[0,4,2,5,1,3,6,7],[0,5,6,4,3,1,2,7],[0,6,7,2,6,2,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
96. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,6,4,0,5],[2,3,7,5,0,6,1,4],[3,7,5,4,1,0,2,6],[4,6,0,1,7,3,5,2],[5,4,6,0,3,2,7,1],[6,0,1,2,5,7,4,3],[7,5,4,6,2,1,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,2,4,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,4,2,0],[0,5,2,6,4,1,3,7],[0,6,4,5,2,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
97. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,6,4,5],[2,3,7,5,1,4,0,6],[3,7,5,6,2,0,1,4],[4,0,1,2,6,7,5,3],[5,6,4,0,7,2,3,1],[6,4,0,1,5,3,7,2],[7,5,6,4,3,1,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,6,6,2,7,0],[0,3,6,1,5,4,2,7],[0,4,6,5,1,3,2,7],[0,5,2,4,3,1,6,7],[0,6,7,2,2,6,7,0],[0,7,0,7,7,7,0,0]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
98. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,5,0,4,6],[2,3,7,6,0,1,5,4],[3,7,6,4,1,2,0,5],[4,5,0,1,7,6,3,2],[5,0,1,2,6,4,7,3],[6,4,5,0,3,7,2,1],[7,6,4,5,2,3,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,4,7,4,2,0],[0,3,4,1,2,6,5,7],[0,4,7,2,7,2,4,0],[0,5,4,6,2,1,3,7],[0,6,2,5,4,3,1,7],[0,7,0,7,0,7,7,0]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
99. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,3,7,0,4,5,6],[2,3,7,6,1,0,4,5],[3,7,6,5,2,1,0,4],[4,0,1,2,5,6,7,3],[5,4,0,1,6,7,3,2],[6,5,4,0,7,3,2,1],[7,6,5,4,3,2,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,7,5,5,7,2,0],[0,3,5,1,6,2,4,7],[0,4,5,6,1,2,3,7],[0,5,7,2,2,7,5,0],[0,6,2,4,3,5,1,7],[0,7,0,7,7,0,7,0]],"subset":[0,1,2,3,4,5,6,7]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], 否, 是, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
100. 有限雙邊理想
子集綁定同一完整有限父環。操作=ideal-trivial-boundary；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,2,4,5,3,6,7,0],[2,4,3,6,5,7,0,1],[3,5,6,0,7,1,2,4],[4,3,5,7,6,0,1,2],[5,6,7,1,0,2,4,3],[6,7,0,2,1,4,3,5],[7,0,1,4,2,3,5,6]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,2,3,4,5,6,7],[0,2,3,0,6,2,3,6],[0,3,0,0,3,3,0,3],[0,4,6,3,1,7,2,5],[0,5,2,3,7,1,6,4],[0,6,3,0,2,6,3,2],[0,7,6,3,5,4,2,1]],"subset":[0]}。請依 [subset,zero_ideal,whole_ring,qualified,boundary] 欄序回答。
查看答案與解釋
([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)
Wave4第二層核對=([0], 是, 否, 是, zero_and_whole_are_always_two_sided_ideals)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；加法子群與左右吸收三責任分開；不混同單側理想子環或抽樣吸收。
本題逐步詳解（AI 二次覆核）
有限雙邊理想 · qf-mod28-ideal-trivial-boundary · candidate
原始題目 JSONL · 驗收報告