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.
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.