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Math Help - Ring Homomorphisms

  1. #1
    Super Member Bernhard's Avatar
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    Ring Homomorphisms

    Determine all ring homomorphisms of  \mathbb{Z} x \mathbb{Z} into  \mathbb{Z} x \mathbb{Z} .

    Clearly justify your method.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Ring Homomorphisms

    Since every element in ZxZ can be written as m(1,0) + n(0,1) for m,n in Z I think every homomorphism would send [ (1,0) to (n,0), (0,1) to (0,m) ]for integers n, m and then theres just the identity homomorphism.
    Last edited by jakncoke; February 19th 2013 at 05:09 PM.
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