Characterizing Baer Modules Over $\tau_q$-Semisimple Rings: An Extension of Baer's Problem

TL;DR

This paper explores the properties of Baer modules over a special class of commutative rings called $ au_q$-semisimple rings, establishing that all such modules are projective, thus extending Baer's problem.

Contribution

It proves that over $ au_q$-semisimple rings, all Baer modules are projective, providing a significant extension to Baer's problem in module theory.

Findings

Baer modules over $ au_q$-semisimple rings are projective

$ au_q$-semisimple rings ensure Baer modules have desirable properties

Extension of Baer's problem to a new class of rings

Abstract

In this note, we investigate the Baer splitting problem over commutative rings. In particular, we show that if a commutative ring $R$ is $\tau_q$-semisimple, then every Baer $R$-module is projective.