A note on projective 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 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.

Keywords

• indecomposable module
• perfect ring
• projective module
• sum-irreducible module