The endomorphism ring of an injective square-free module

TL;DR

This paper characterizes when the endomorphism ring of an injective square-free module is quasi-duo, establishing a precise equivalence with the module being square-free.

Contribution

It proves that the endomorphism ring of an injective module is quasi-duo if and only if the module is square-free, providing a new characterization in module theory.

Findings

Endomorphism ring is quasi-duo iff the module is square-free

Provides a characterization linking module properties to ring properties

Enhances understanding of the structure of injective modules

Abstract

Let $M_R$ be an injective right module over a ring $R$. The goal of this paper to prove that the endomorphism ring $S=(M_R)$ of $M$ is quasi-duo if and only if $M_R$ is square-free.