English

Modules with commutative endomorphism rings

Commutative Algebra 2024-09-10 v3

Abstract

In this paper we review and study RR-modules MM for which S=EndR(M)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.

Keywords

Cite

@article{arxiv.2309.15219,
  title  = {Modules with commutative endomorphism rings},
  author = {Sayed Malek Javdannezhad},
  journal= {arXiv preprint arXiv:2309.15219},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-28T12:33:08.513Z