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Math Help - Integral Domain

  1. #1
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    Integral Domain

    Let A and B be rings, and f: A -> B a homomorphism.

    Prove that if B is an integral domain, then either f(1)=1 or f(1)=0.

    I have no clue any advice?
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  2. #2
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    Re: Integral Domain

    we have f(1) = f((1)(1)) = f(1)f(1).

    thus f(1)f(1) - f(1) = 0,

    so f(1)(f(1) - 1) = 0. can you continue?
    Thanks from jzellt
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  3. #3
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    Re: Integral Domain

    Awesome! You're great man.
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