Centrally endo-AIP Modules

Abstract

In this paper, we introduce the concept of centrally endo-AIP modules. We call a module M centrally endo-AIP, if the left annihilator of any fully invariant submodule N of M in the endomorphism ring S = End(M) is a centrally s-unital ideal of S. We discuss some properties of centrally endo-AIP modules. We also study the endomorphism ring of centrally endo-AIP modules and characterize quasi-Baer modules in terms of centrally endo-AIP modules