Centrally endo-AIP Modules

TL;DR

This paper introduces centrally endo-AIP modules, exploring their properties, endomorphism rings, and their relation to quasi-Baer modules, advancing the understanding of module theory and endomorphism ring structures.

Contribution

It defines the concept of centrally endo-AIP modules and characterizes their properties and relation to quasi-Baer modules, providing new insights into module and ring theory.

Findings

Centrally endo-AIP modules have specific properties related to their endomorphism rings.

The endomorphism ring of such modules exhibits particular structural features.

Quasi-Baer modules can be characterized using 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