Every nite domain contains an identity element.

[Stephen88]

Homework Statement

I'm trying to write a proof ot demonstrate that every finite domain contains
an identity element.

Homework Equations

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?

 

[Stephen88]

Oh wait but I can manipulate the numbers as I want...I can write x=y*d and y=y*e(this means that y doesn't have to be from the domain because I haven't proved the identity part) and =>x=y*e*d=>x=e*x=>e is and identity element in the domain.Will this work?