A Note on Projective Modules
Hossein Faridian
TL;DR
This paper explores the theory of projective modules over perfect rings, providing a characterization of indecomposable projective modules and establishing a correspondence with simple modules.
Contribution
It offers a new characterization of indecomposable projective modules and links them directly to simple modules over perfect rings.
Findings
Characterization of indecomposable projective modules
One-to-one correspondence with simple modules
Extension of theory similar to injective modules
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 , we present a characterization of indecomposable projective -modules and describe a one-to-one correspondence between the projective indecomposable -modules and the simple -modules.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Advanced Topics in Algebra