1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook