# Concept derivation guides

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Concept guide



## [Finite unital ring: proving that the mod-4 addition and multiplication tables form a unital ring](/en/derivations/derivation-mko-finite-unital-ring-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-finite-unital-ring)

On the carrier X={0,1,2,3}, complete addition and multiplication tables ⊕ and ⊙ (addition and multiplication mod 4) are given. Prove for all pairs and triples: (X,⊕) is an abelian group; ⊙ is associative; ⊙ distributes over ⊕ on both sides; there is a unique two-sided multiplicative identity 1, and 1≠0. Note also that 2⊙2=0 does not stop it from being a unital ring.

Finite unital ring

derivation-mko-finite-unital-ring-01





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