A Note on Projective Modules

2020/11/16 by Hossein Faridian, Faridian, Hossein
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2011.08086

openalex publication_date 2020/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This expository note delves into the theory of projective modules parallel to the one developed for injective modules by Matlis. Given a perfect ring R, we present a characterization of indecomposable projective R-modules and describe a one-to-one correspondence between the projective indecomposable R-modules and the simple R-modules.

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