# Concept derivation guides

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Concept guide



## [Finite integral domain: deciding ℤ/5ℤ and ℤ/6ℤ from complete tables, then deriving invertibility from finiteness](/en/derivations/derivation-mko-finite-integral-domain-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-finite-integral-domain)

Using complete multiplication tables, decide that ℤ/5ℤ is a finite integral domain and ℤ/6ℤ is not; then prove, as a theorem that comes after the definition, that every nonzero element of any finite integral domain is invertible, using finiteness; find all inverses in ℤ/5ℤ and explain why 2 has no inverse in ℤ/6ℤ.

Finite integral domain

derivation-mko-finite-integral-domain-01





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