ON GENERALIZATION OF circle plus-COFINITELY SUPPLEMENTED MODULES

Abstract

We study the properties of circle plus-cofinitely radical supplemented modules, or, briefly, cgs(circle plus)-modules. It is shown that a module with summand sum property (SSP) is cgs(circle plus) if and only if M/w Loc(circle plus) M (w Loc(circle plus) 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(circle plus)-module is cgs(circle plus), and that, for any ring R, every free R-module is cgs(circle plus) if and only if R is semiperfect.