MODULES WITH THE PROPERTY Radg

Abstract

In this article, we introduce modules with the property Radg and provide various properties of this module. Firstly, we prove that every semisimple module has the property Radg. We also indicate that the class of modules with the property Radg is closed under finite direct sum and direct summands. Moreover, we define the concepts of g –(radical) cover. We show that factor modules of a module with the property Radg have the property Radg under special condition. Additionally, we characterize semisimple commutative rings via modules with the property Radg.