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
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?
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?
Awesome! You're great man.