Projective Modules over Dedekind Domains
نویسنده
چکیده
In these notes we will first define projective modules and prove some standard properties of those modules. Then we will classify finitely generated projective modules over Dedekind domains Remark 0.1. All rings will be commutative with 1. 1. Projective modules Definition 1.1. Let R be a ring and let M be an R-module. Then M is called projective if for all surjections p : N → N ′ and a map f : M → N ′ there is a map g : M → N such that p ◦ g = f . In a diagram:
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