Socle-regular -modules

Abstract

A right module over an associative ring with unity is a -module if every finitely generated submodule of any homomorphic image of is a direct sum of uniserial modules. In this paper we focus our attention to the socles of fully invariant submodules and introduce a new class of modules, which we term socle-regular -modules. This class is shown to be large and strictly contains the class of fully transitive modules. Also, here we investigated some basic properties of such modules