If F and G are free modules, and if F dual is isomorphic to G dual, does that imply that F is isomorphic to G? By dual of a module H I mean Hom(H,R) where H is an R module.
Duals of free modules are isomorphic implies modules are isomorphic
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commutative-algebra
modules
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0For finitely generated modules, yes. – 2017-02-06
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0Yes, in general? – 2017-02-06
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0When speaking about duals in commutative algebra, one should say which kind of duals one talks about. The naive analog of the 'vector space'-dual, i.e. $\operatorname{Hom}_R(-,R)$, is rarely used and thus not the only notion of a dual module. – 2017-02-08
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0Oh, yes I mean dual in the sense of dual of a vector space, I.e. Hom(F,R) where F is an R module – 2017-02-08