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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- Nov 14th 2012, 09:14 PMjzelltIntegral 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? - Nov 14th 2012, 11:38 PMDevenoRe: 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? - Nov 14th 2012, 11:44 PMjzelltRe: Integral Domain
Awesome! You're great man.