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Ideal and factor ring problem

  1. Nov 28, 2007 #1
    1. The problem statement, all variables and given/known data

    If A is an ideal of a ring R and 1 belongs to A, prove that A=R.

    2. Relevant equations

    3. The attempt at a solution

    I said that r should an element of R. and since A is ideal to ring R and 1 is an element of A , then ar should be an element of A . 1 must be an element of a which is an element of ar which is an element of A. Therefore 1*ra=ar*1=> 1 is an element of R. Therefore,R=A
  2. jcsd
  3. Nov 28, 2007 #2


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    1 must be an element of a doesn't mean anything... what the heck is a supposed to be anyway? I'm assuming it's an element of A maybe... at any rate, nothing can be an element of ar as ar is simply a member of the ring, and you have no reason to believe it's a set.

    You realize an ideal is defined such that if a is in A, then for all x in R, x*a is in A?
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