Revista de la
Unión Matemática Argentina
On Baer modules
Chillumuntala Jayaram, Ünsal Tekir, and Suat Koç
Volume 63, no. 1 (2022), pp. 109–128

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A commutative ring $R$ is said to be a Baer ring if for each $a\in R$, $\operatorname{ann}(a)$ is generated by an idempotent element $b\in R$. In this paper, we extend the notion of a Baer ring to modules in terms of weak idempotent elements defined in a previous work by Jayaram and Tekir. Let $R$ be a commutative ring with a nonzero identity and let $M$ be a unital $R$-module. $M$ is said to be a Baer module if for each $m\in M$ there exists a weak idempotent element $e\in R$ such that $\operatorname{ann}_{R}(m)M=eM$. Various examples and properties of Baer modules are given. Also, we characterize a certain class of modules/submodules such as von Neumann regular modules/prime submodules in terms of Baer modules.