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?

Printable View

- November 14th 2012, 10:14 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? - November 15th 2012, 12:38 AMDevenoRe: 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? - November 15th 2012, 12:44 AMjzelltRe: Integral Domain
Awesome! You're great man.