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.

On a Generalization of Cofinitely Lifting Modules

“…Example 2.8. (see [13], Example 2.2) Let M be a biuniform module and S = End(M ). Suppose that P is the projective S-module with dim(P ) = (1, 0).…”

“…On the other hand, M is called (cofinitely) Rad-⊕-supplemented if every (cofinite) submodule of M has a Rad-supplement that is a direct summand of M . By cgs ⊕ , we denote cofinitely Rad-⊕-supplemented modules in [13].…”

“…is a cofinitely lifting module. 8Z are local, M is a cgs ⊕ -module according to[13, Theorem 2.1]. Note that M is finitely generated.…”

Some Properties of $\oplus -$ Cofinitely $\delta -$s Supplemented Modules

“…Basic properties of these modules we refer to [10,11]. Another generalization of these modules was studied in [12].…”