Concept guide
Finite unital ring: proving that the mod-4 addition and multiplication tables form a 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.