Free modules, finitely-generated modules
نویسنده
چکیده
The following definition is an example of defining things by mapping properties, that is, by the way the object relates to other objects, rather than by internal structure. The first proposition, which says that there is at most one such thing, is typical, as is its proof. Let R be a commutative ring with 1. Let S be a set. A free R-moduleM on generators S is an R-module M and a set map i : S → M such that, for any R-module N and any set map f : S → N , there is a unique R-module homomorphism f̃ : M → N such that
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