1. The problem statement, all variables and given/known data I'm trying to write a proof ot demonstrate that every finite domain contains an identity element. 2. Relevant equations 3. The attempt at a solution If I can think of the operation from the ring as a mapping...like x->yx..where y are just values from the domain and then to consider the possibility that for one y from the domain the following happens x=xy then maybe this will work.But not for addition How should I think about this problem?