Modules with commutative endomorphism rings

Abstract

In this paper we review and study $R$-modules $M$ for which $S=En{d}_R(M)$ 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.

arXiv commentThe paper has some non valid results and should be revised. Since it takes some times, I prefer to withdraw it. Best Regards