On Goldie-Supplemented Modules

Abstract

Let M be a left R-module. X,Y of M are beta* equivalent, X beta*Y , if and only if X+Y X is small in MX and X+Y Y is small in MY . A module M is called G*-supplemented if for every submodule X of M there is a supplement submodule S of M such that X beta*S. In this work some new properties of beta* are given and G*-supplemented modules are studied. Also completely G*-supplemented modules and G*-radical supplemented modules are defined.