Modules Having a Weak Rad-Supplement in Every Cofinite Extension

Abstract

In this study, we introduce the modules with the properties (CWRE) and (CWREE) as a generalization of the modules with the properties (CWE) and (CWEE). Let R be a ring and M be a left R-module. If M has the property (CWRE), then every direct summand of M has the property (CWRE). A ring R is semilocal if and only if every left R-module has the property (CWRE). We also study the modules that have the properties (WRE*) and (WREE*). A module has the property (WREE*) if and only if every submodule of it has the property (WRE*).