A GENERALIZATION OF g-SUPPLEMENTED MODULES

Abstract

In this work g-radical supplemented modules are defined which generalize g-supplemented modules. Some properties of g-radical supplemented modules are investigated. It is proved that the finite sum of g-radical supplemented modules is g-radical supplemented. It is also proved that every factor module and every homomorphic image of a g-radical supplemented module is g-radical supplemented. Let R be a ring. Then R-R is g-radical supplemented if and only if every finitely generated R-module is g-radical supplemented. In the end of this work, it is given two examples for g-radical supplemented modules separating with g-supplemented modules.