# Math Help - Integral Domain

1. ## 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?

2. ## 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?

3. ## Re: Integral Domain

Awesome! You're great man.