Modules in which semisimple fully invariant submodules are essential in summands

Abstract

One of the useful generalization of extending notion is FI -extending property. A module is called FI -extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak FI -extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules.To this end, we call such a module Weak FI -extending. We obtain that FI -extending modules are properly containedin this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summandsof Weak FI -extending modules.