Modules with the Property Radg

Abstract

In this article, we introduce modules with the property Rad(g) and provide various properties of this module. Firstly, we prove that every semisimple module has the property Rad(g). We also indicate that the class of modules with the property Rad(g) 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 Rad(g) under special condition. Additionally, we characterize semisimple commutative rings via modules with the property Rad(g).