Goldie extending property on the class of exact submodules

Abstract

We define a module M to be G'-extending if for each exact submodule X of M there exists a direct summand D of M such that X boolean AND D is essential in both X and D. We investigate G'-extending modules and locate the implications between the other extending properties. We study decomposition theory and extensions for G'-extending concept. We show that if a ring is right G'-extending, then so its essential overring. It is shown that G'-extending property is inherited by its rational hull. We provide examples by making special choices of left exact preradicals.