Hi there,
I would like some help with the following:
Let f be a homomorphism between two commutative rings A and B. S is a multiplicatively closed subset of A. Then f(S) is a multiplicatively closed subset of B. Now the book says that S(^-1)B and (f(S)^-1)B are isomorphic as S(^-1)A-modules.
I get that we can see B as an A-module and from there that S(^-1)B is an S(^-1)A-module. But why is (f(S)^-1)B an S(^-1)A-module?
J.