Modules with commutative endomorphism rings

TL;DR

This paper investigates modules with commutative endomorphism rings, introducing the concept of the center of modules, and explores properties, submodules, direct products, and the endo-commutativity dimension to deepen understanding of their structure.

Contribution

It introduces the concept of the center of modules and studies modules with commutative endomorphism rings, including properties and the endo-commutativity dimension.

Findings

Defined the center of modules as a generalization of ring centers

Analyzed properties of modules with commutative endomorphism rings

Introduced the concept of endo-commutativity dimension

Abstract

In this paper we review and study $R$-modules $M$ for which $S = End_R(M)$ is commutative. For this, we define the concept of center of modules which is a natural generalization of the center of rings. The properties of center of modules, submodules and direct products and also, modules whose bi-endomorphism rings are commutative, have been considered. More generally, we study the sequence of the endomorphism rings and define the endo-commutativity dimension of modules.