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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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?
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