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Every nite domain contains an identity element.

  1. Mar 9, 2012 #1
    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?
     
  2. jcsd
  3. Mar 9, 2012 #2
    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?
     
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