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Published
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On Baer modules
Volume 63, no. 1
(2022),
pp. 109–128
https://doi.org/10.33044/revuma.1741
Abstract
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.
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Published by the Unión Matemática Argentina |
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