有限交換環基礎 · 脈衝 R01
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-r01-finite-commutative-ring-foundations · 2026-10-14 · 100 題
1. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,0,3,2,5,4,7,6],[2,3,0,1,6,7,4,5],[3,2,1,0,7,6,5,4],[4,5,6,7,0,1,2,3],[5,4,7,6,1,0,3,2],[6,7,4,5,2,3,0,1],[7,6,5,4,3,2,1,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,0,1,0,1,0,1],[0,2,0,2,0,2,0,2],[0,3,0,3,0,3,0,3],[0,0,2,2,4,4,6,6],[0,1,2,3,4,5,6,7],[0,2,2,0,4,6,6,4],[0,3,2,1,4,7,6,5]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 5, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 6, 0, 2], [1, 7, 1, 3], [2, 3, 2, 0], [2, 4, 0, 2], [2, 6, 0, 2], [3, 4, 0, 2], [3, 7, 3, 1], [4, 6, 6, 4], [4, 7, 6, 4], [6, 7, 4, 6]], 否, unital_ring_not_commutative)
Wave4第二層核對=(8, 0, 5, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 6, 0, 2], [1, 7, 1, 3], [2, 3, 2, 0], [2, 4, 0, 2], [2, 6, 0, 2], [3, 4, 0, 2], [3, 7, 3, 1], [4, 6, 6, 4], [4, 7, 6, 4], [6, 7, 4, 6]], 否, unital_ring_not_commutative)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
2. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
3. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
4. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
5. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
6. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,0,3,2,7,6,5,4],[2,3,0,1,6,7,4,5],[3,2,1,0,5,4,7,6],[4,7,6,5,0,3,2,1],[5,6,7,4,3,0,1,2],[6,5,4,7,2,1,0,3],[7,4,5,6,1,2,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,0,1,0,1,0,1],[0,2,0,2,0,2,0,2],[0,3,0,3,0,3,0,3],[0,0,2,2,4,6,6,4],[0,3,2,1,4,7,6,5],[0,2,2,0,4,4,6,6],[0,1,2,3,4,5,6,7]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 7, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 5, 1, 3], [1, 6, 0, 2], [2, 3, 2, 0], [2, 4, 0, 2], [2, 6, 0, 2], [3, 4, 0, 2], [3, 5, 3, 1], [4, 5, 6, 4], [4, 6, 6, 4], [5, 6, 6, 4]], 否, unital_ring_not_commutative)
Wave4第二層核對=(8, 0, 7, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 5, 1, 3], [1, 6, 0, 2], [2, 3, 2, 0], [2, 4, 0, 2], [2, 6, 0, 2], [3, 4, 0, 2], [3, 5, 3, 1], [4, 5, 6, 4], [4, 6, 6, 4], [5, 6, 6, 4]], 否, unital_ring_not_commutative)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
7. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
8. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
9. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
10. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
11. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,0,3,2,6,7,4,5],[2,3,0,1,5,4,7,6],[3,2,1,0,7,6,5,4],[4,6,5,7,0,2,1,3],[5,7,4,6,2,0,3,1],[6,4,7,5,1,3,0,2],[7,5,6,4,3,1,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,0,1,0,0,1,1],[0,2,0,2,0,0,2,2],[0,3,0,3,0,0,3,3],[0,2,2,0,4,5,5,4],[0,0,2,2,4,5,4,5],[0,3,2,1,4,5,7,6],[0,1,2,3,4,5,6,7]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 7, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 4, 0, 2], [1, 6, 1, 3], [2, 3, 2, 0], [2, 4, 0, 2], [2, 5, 0, 2], [3, 5, 0, 2], [3, 6, 3, 1], [4, 5, 5, 4], [4, 6, 5, 4], [5, 6, 4, 5]], 否, unital_ring_not_commutative)
Wave4第二層核對=(8, 0, 7, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 4, 0, 2], [1, 6, 1, 3], [2, 3, 2, 0], [2, 4, 0, 2], [2, 5, 0, 2], [3, 5, 0, 2], [3, 6, 3, 1], [4, 5, 5, 4], [4, 6, 5, 4], [5, 6, 4, 5]], 否, unital_ring_not_commutative)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
12. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
13. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
14. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
15. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
16. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,0,3,2,7,6,5,4],[2,3,0,1,5,4,7,6],[3,2,1,0,6,7,4,5],[4,7,5,6,0,2,3,1],[5,6,4,7,2,0,1,3],[6,5,7,4,3,1,0,2],[7,4,6,5,1,3,2,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,0,1,1,1,0,0],[0,2,0,2,2,2,0,0],[0,3,0,3,3,3,0,0],[0,3,2,1,5,4,6,7],[0,1,2,3,4,5,6,7],[0,0,2,2,7,6,6,7],[0,2,2,0,6,7,6,7]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 5, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 4, 1, 3], [1, 7, 0, 2], [2, 3, 2, 0], [2, 6, 0, 2], [2, 7, 0, 2], [3, 4, 3, 1], [3, 6, 0, 2], [4, 6, 6, 7], [4, 7, 7, 6], [6, 7, 7, 6]], 否, unital_ring_not_commutative)
Wave4第二層核對=(8, 0, 5, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 4, 1, 3], [1, 7, 0, 2], [2, 3, 2, 0], [2, 6, 0, 2], [2, 7, 0, 2], [3, 4, 3, 1], [3, 6, 0, 2], [4, 6, 6, 7], [4, 7, 7, 6], [6, 7, 7, 6]], 否, unital_ring_not_commutative)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
17. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
18. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
19. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
20. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
21. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-qualification；資料={"n":8,"addition":[[0,1,2,3,4,5,6,7],[1,0,3,2,6,7,4,5],[2,3,0,1,7,6,5,4],[3,2,1,0,5,4,7,6],[4,6,7,5,0,3,1,2],[5,7,6,4,3,0,2,1],[6,4,5,7,1,2,0,3],[7,5,4,6,2,1,3,0]],"multiplication":[[0,0,0,0,0,0,0,0],[0,1,0,1,0,1,1,0],[0,2,0,2,0,2,2,0],[0,3,0,3,0,3,3,0],[0,2,2,0,4,4,7,7],[0,1,2,3,4,5,6,7],[0,3,2,1,4,6,5,7],[0,0,2,2,4,7,4,7]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 5, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 4, 0, 2], [1, 6, 1, 3], [2, 3, 2, 0], [2, 4, 0, 2], [2, 7, 0, 2], [3, 6, 3, 1], [3, 7, 0, 2], [4, 6, 7, 4], [4, 7, 7, 4], [6, 7, 7, 4]], 否, unital_ring_not_commutative)
Wave4第二層核對=(8, 0, 5, [[1, 2, 0, 2], [1, 3, 1, 3], [1, 4, 0, 2], [1, 6, 1, 3], [2, 3, 2, 0], [2, 4, 0, 2], [2, 7, 0, 2], [3, 6, 3, 1], [3, 7, 0, 2], [4, 6, 7, 4], [4, 7, 7, 4], [6, 7, 7, 4]], 否, unital_ring_not_commutative)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
22. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
23. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
24. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
25. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-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]]}。請依 [n,zero,one,noncommuting_pairs,commutative,classification] 欄序回答。
查看答案與解釋
(8, 0, 1, [], 是, commutative_ring)
Wave4第二層核對=(8, 0, 1, [], 是, commutative_ring)；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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-qualification · candidate
26. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":1,"b":2}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(1, 2, 2, 2, 是)
Wave4第二層核對=(1, 2, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
27. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":2,"b":5}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(2, 5, 2, 2, 是)
Wave4第二層核對=(2, 5, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
28. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":3,"b":0}。請依 [a,b,ab,ba,equal] 欄序回答。
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(3, 0, 0, 0, 是)
Wave4第二層核對=(3, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
29. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":4,"b":3}。請依 [a,b,ab,ba,equal] 欄序回答。
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(4, 3, 4, 4, 是)
Wave4第二層核對=(4, 3, 4, 4, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
30. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":7,"b":5}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(7, 5, 5, 5, 是)
Wave4第二層核對=(7, 5, 5, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
31. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":6,"b":1}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(6, 1, 6, 6, 是)
Wave4第二層核對=(6, 1, 6, 6, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
32. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":7,"b":5}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(7, 5, 5, 5, 是)
Wave4第二層核對=(7, 5, 5, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
33. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":0,"b":6}。請依 [a,b,ab,ba,equal] 欄序回答。
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(0, 6, 0, 0, 是)
Wave4第二層核對=(0, 6, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
34. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":1,"b":2}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(1, 2, 2, 2, 是)
Wave4第二層核對=(1, 2, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
35. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":2,"b":6}。請依 [a,b,ab,ba,equal] 欄序回答。
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(2, 6, 2, 2, 是)
Wave4第二層核對=(2, 6, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
36. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":3,"b":0}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(3, 0, 0, 0, 是)
Wave4第二層核對=(3, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
37. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":5,"b":3}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(5, 3, 5, 5, 是)
Wave4第二層核對=(5, 3, 5, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
38. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":4,"b":5}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(4, 5, 5, 5, 是)
Wave4第二層核對=(4, 5, 5, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
39. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":7,"b":1}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(7, 1, 7, 7, 是)
Wave4第二層核對=(7, 1, 7, 7, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
40. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":7,"b":6}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(7, 6, 6, 6, 是)
Wave4第二層核對=(7, 6, 6, 6, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
41. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":0,"b":4}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(0, 4, 0, 0, 是)
Wave4第二層核對=(0, 4, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
42. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":1,"b":2}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(1, 2, 2, 2, 是)
Wave4第二層核對=(1, 2, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
43. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":2,"b":7}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(2, 7, 2, 2, 是)
Wave4第二層核對=(2, 7, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
44. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":3,"b":0}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(3, 0, 0, 0, 是)
Wave4第二層核對=(3, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
45. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":7,"b":3}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(7, 3, 7, 7, 是)
Wave4第二層核對=(7, 3, 7, 7, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
46. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":5,"b":4}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(5, 4, 4, 4, 是)
Wave4第二層核對=(5, 4, 4, 4, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
47. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":6,"b":1}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(6, 1, 6, 6, 是)
Wave4第二層核對=(6, 1, 6, 6, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
48. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":5,"b":7}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(5, 7, 7, 7, 是)
Wave4第二層核對=(5, 7, 7, 7, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
49. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":0,"b":4}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(0, 4, 0, 0, 是)
Wave4第二層核對=(0, 4, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
50. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-product-swap；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]],"a":1,"b":2}。請依 [a,b,ab,ba,equal] 欄序回答。
查看答案與解釋
(1, 2, 2, 2, 是)
Wave4第二層核對=(1, 2, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-product-swap · candidate
51. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":1,"b":2,"exponent":1}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(1, 2, 1, 2, 2, 2, 是)
Wave4第二層核對=(1, 2, 1, 2, 2, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
52. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":2,"b":5,"exponent":2}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(2, 5, 2, 2, 4, 4, 是)
Wave4第二層核對=(2, 5, 2, 2, 4, 4, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
53. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":3,"b":0,"exponent":3}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(3, 0, 3, 0, 0, 0, 是)
Wave4第二層核對=(3, 0, 3, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
54. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":4,"b":3,"exponent":4}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(4, 3, 4, 4, 0, 0, 是)
Wave4第二層核對=(4, 3, 4, 4, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
55. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":7,"b":5,"exponent":5}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(7, 5, 5, 5, 0, 0, 是)
Wave4第二層核對=(7, 5, 5, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
56. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":6,"b":1,"exponent":6}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(6, 1, 6, 6, 0, 0, 是)
Wave4第二層核對=(6, 1, 6, 6, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
57. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":7,"b":5,"exponent":7}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(7, 5, 7, 5, 0, 0, 是)
Wave4第二層核對=(7, 5, 7, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
58. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":0,"b":6,"exponent":1}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(0, 6, 1, 0, 0, 0, 是)
Wave4第二層核對=(0, 6, 1, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
59. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":1,"b":2,"exponent":2}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(1, 2, 2, 2, 5, 5, 是)
Wave4第二層核對=(1, 2, 2, 2, 5, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
60. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":2,"b":6,"exponent":3}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(2, 6, 3, 2, 0, 0, 是)
Wave4第二層核對=(2, 6, 3, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
61. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":3,"b":0,"exponent":4}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(3, 0, 4, 0, 0, 0, 是)
Wave4第二層核對=(3, 0, 4, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
62. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":5,"b":3,"exponent":5}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(5, 3, 5, 5, 0, 0, 是)
Wave4第二層核對=(5, 3, 5, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
63. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":4,"b":5,"exponent":6}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(4, 5, 6, 5, 0, 0, 是)
Wave4第二層核對=(4, 5, 6, 5, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
64. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":7,"b":1,"exponent":7}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(7, 1, 7, 7, 0, 0, 是)
Wave4第二層核對=(7, 1, 7, 7, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
65. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":7,"b":6,"exponent":1}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(7, 6, 1, 6, 6, 6, 是)
Wave4第二層核對=(7, 6, 1, 6, 6, 6, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
66. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":0,"b":4,"exponent":2}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(0, 4, 2, 0, 0, 0, 是)
Wave4第二層核對=(0, 4, 2, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
67. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":1,"b":2,"exponent":3}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(1, 2, 3, 2, 0, 0, 是)
Wave4第二層核對=(1, 2, 3, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
68. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":2,"b":7,"exponent":4}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(2, 7, 4, 2, 0, 0, 是)
Wave4第二層核對=(2, 7, 4, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
69. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":3,"b":0,"exponent":5}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(3, 0, 5, 0, 0, 0, 是)
Wave4第二層核對=(3, 0, 5, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
70. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":7,"b":3,"exponent":6}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(7, 3, 6, 7, 0, 0, 是)
Wave4第二層核對=(7, 3, 6, 7, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
71. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":5,"b":4,"exponent":7}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
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(5, 4, 7, 4, 0, 0, 是)
Wave4第二層核對=(5, 4, 7, 4, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
72. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":6,"b":1,"exponent":1}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(6, 1, 1, 6, 6, 6, 是)
Wave4第二層核對=(6, 1, 1, 6, 6, 6, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
73. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":5,"b":7,"exponent":2}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(5, 7, 2, 7, 0, 0, 是)
Wave4第二層核對=(5, 7, 2, 7, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
74. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":0,"b":4,"exponent":3}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(0, 4, 3, 0, 0, 0, 是)
Wave4第二層核對=(0, 4, 3, 0, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
75. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-power-product；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]],"a":1,"b":2,"exponent":4}。請依 [a,b,exponent,ab,lhs,rhs,equal] 欄序回答。
查看答案與解釋
(1, 2, 4, 2, 0, 0, 是)
Wave4第二層核對=(1, 2, 4, 2, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-power-product · candidate
76. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":1,"b":2}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(1, 2, 3, 1, 1, 2, 4, 1, 是)
Wave4第二層核對=(1, 2, 3, 1, 1, 2, 4, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
77. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":2,"b":5}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(2, 5, 6, 1, 4, 2, 1, 1, 是)
Wave4第二層核對=(2, 5, 6, 1, 4, 2, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
78. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":3,"b":0}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(3, 0, 3, 1, 1, 0, 0, 1, 是)
Wave4第二層核對=(3, 0, 3, 1, 1, 0, 0, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
79. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":4,"b":3}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(4, 3, 5, 1, 0, 4, 1, 1, 是)
Wave4第二層核對=(4, 3, 5, 1, 0, 4, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
80. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":7,"b":5}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(7, 5, 3, 1, 1, 5, 4, 1, 是)
Wave4第二層核對=(7, 5, 3, 1, 1, 5, 4, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
81. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":6,"b":1}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(6, 1, 5, 1, 4, 6, 1, 1, 是)
Wave4第二層核對=(6, 1, 5, 1, 4, 6, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
82. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":7,"b":5}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(7, 5, 3, 1, 1, 5, 0, 1, 是)
Wave4第二層核對=(7, 5, 3, 1, 1, 5, 0, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
83. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":0,"b":6}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(0, 6, 6, 1, 0, 0, 1, 1, 是)
Wave4第二層核對=(0, 6, 6, 1, 0, 0, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
84. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":1,"b":2}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(1, 2, 3, 1, 1, 2, 5, 1, 是)
Wave4第二層核對=(1, 2, 3, 1, 1, 2, 5, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
85. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":2,"b":6}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(2, 6, 4, 1, 5, 2, 1, 1, 是)
Wave4第二層核對=(2, 6, 4, 1, 5, 2, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
86. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":3,"b":0}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(3, 0, 3, 1, 1, 0, 0, 1, 是)
Wave4第二層核對=(3, 0, 3, 1, 1, 0, 0, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
87. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":5,"b":3}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(5, 3, 4, 1, 0, 5, 1, 1, 是)
Wave4第二層核對=(5, 3, 4, 1, 0, 5, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
88. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":4,"b":5}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(4, 5, 3, 1, 1, 5, 6, 1, 是)
Wave4第二層核對=(4, 5, 3, 1, 1, 5, 6, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
89. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":7,"b":1}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(7, 1, 5, 1, 6, 7, 1, 1, 是)
Wave4第二層核對=(7, 1, 5, 1, 6, 7, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
90. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":7,"b":6}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(7, 6, 3, 1, 1, 6, 0, 1, 是)
Wave4第二層核對=(7, 6, 3, 1, 1, 6, 0, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
91. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":0,"b":4}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(0, 4, 4, 1, 0, 0, 1, 1, 是)
Wave4第二層核對=(0, 4, 4, 1, 0, 0, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
92. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":1,"b":2}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(1, 2, 3, 1, 1, 2, 6, 1, 是)
Wave4第二層核對=(1, 2, 3, 1, 1, 2, 6, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
93. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":2,"b":7}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(2, 7, 4, 1, 6, 2, 1, 1, 是)
Wave4第二層核對=(2, 7, 4, 1, 6, 2, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
94. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":3,"b":0}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(3, 0, 3, 1, 1, 0, 0, 1, 是)
Wave4第二層核對=(3, 0, 3, 1, 1, 0, 0, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
95. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":7,"b":3}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(7, 3, 5, 1, 0, 7, 1, 1, 是)
Wave4第二層核對=(7, 3, 5, 1, 0, 7, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
96. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":5,"b":4}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(5, 4, 3, 1, 1, 4, 7, 1, 是)
Wave4第二層核對=(5, 4, 3, 1, 1, 4, 7, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
97. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":6,"b":1}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
查看答案與解釋
(6, 1, 4, 1, 7, 6, 1, 1, 是)
Wave4第二層核對=(6, 1, 4, 1, 7, 6, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
98. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":5,"b":7}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
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(5, 7, 3, 1, 1, 7, 0, 1, 是)
Wave4第二層核對=(5, 7, 3, 1, 1, 7, 0, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
99. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":0,"b":4}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
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(0, 4, 4, 1, 0, 0, 1, 1, 是)
Wave4第二層核對=(0, 4, 4, 1, 0, 0, 1, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
100. 有限交換環
同一完整有限含一環的加法表與乘法表。操作=commring-binomial-square；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]],"a":1,"b":2}。請依 [a,b,sum,lhs,a2,ab,b2,rhs,equal] 欄序回答。
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(1, 2, 4, 1, 1, 2, 3, 1, 是)
Wave4第二層核對=(1, 2, 4, 1, 1, 2, 3, 1, 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；乘法交換律逐全部元素對核對；交換環不自動是整環或域且可有零因子。
本題逐步詳解（AI 二次覆核）
有限交換環 · qf-mod28-commring-binomial-square · candidate
原始題目 JSONL · 驗收報告