math8
Dec31-08, 03:43 PM
17034
Let R be a commutative ring with 1. If F is a free module of rank n < 1, then show that
HomR(F;M) is isomorphic to M^n, for each R-module M.
I was thinking about defining a map
Psi : HomR(F;M)--> M^n by psi(f) = (f(e1); f(e2); ... ; f(en))
where F is free on (e1; ... ; en) and
show Psi is an isomorphism. But I am having difficulties showing it is onto.
Let R be a commutative ring with 1. If F is a free module of rank n < 1, then show that
HomR(F;M) is isomorphic to M^n, for each R-module M.
I was thinking about defining a map
Psi : HomR(F;M)--> M^n by psi(f) = (f(e1); f(e2); ... ; f(en))
where F is free on (e1; ... ; en) and
show Psi is an isomorphism. But I am having difficulties showing it is onto.