Socle-Regular QTAG-Modules

A right module M over an associative ring with unity is a QTAG-module if every ?nitely generated submodule of any homomorphic image of M 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 QTAG-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.