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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.

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# Homework Help: Free modules

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