Cofinitely Weak Supplemented Modules

Abstract

We prove that a module M is cofinitely weak supplemented or briefly cws (i.e., every submodule N of M with M/N finitely generated, has a weak supplement) if and only if every maximal submodule has a weak supplement. If M is a cws-module then every M-generated module is a cws-module. Every module is cws if and only if the ring is semilocal. We study also modules, whose finitely generated submodules have weak supplements.

Key Words:

• Cofinite submodule
• Cofinitely weak supplemented module
• Finitely weak supplemented module

AMS Classification Numbers:

• 16D10
• 16L30
• 16D99

Acknowledgments

This paper was written during the visit of the first author to Izmir Institute of Technology under a grant from TÜBİTAK. Authors would like to express their gratitude to TÜBİTAK for its support. Special thanks are due to the referee for the valuable comments and suggestions.