1. Let E denote the set of even integers. Prove that with the usual addidion, and with multiplication defined by m*n=(1/2)mn, E is a ring. Is there a unity?
2. Prove that aČ-bČ=(a+b)(a-b) for all a,b in a ring R iff R is commutative.
I'm new to rings and am unsure how to get going with these problems. Any help would be great.