On Generalization of ⊕-Cofinitely Supplemented Modules

Abstract

We study the properties of ⊕-cofinitely radical supplemented modules, or, briefly, cgs⊕-modules. It is shown that a module with summand sum property (SSP) is cgs⊕ if and only if M/w Loc⊕M (w Loc⊕M is the sum of all w-local direct summands of a module M) does not contain any maximal submodule, that every cofinite direct summand of a UC-extending cgs⊕-module is cgs⊕, and that, for any ring R, every free R-module is cgs⊕ if and only if R is semiperfect. © 2010 Springer Science+Business Media, Inc.