Baer submodules of modules over commutative rings

Adam Anebrı; Hwankoo Kım; Najib Mahdou

doi:10.24330/ieja.1252741

Research Article

Baer submodules of modules over commutative rings

Year 2023, , 31 - 47, 10.07.2023

Adam Anebrı Hwankoo Kım Najib Mahdou

https://doi.org/10.24330/ieja.1252741

Abstract

Let $R$ be a commutative ring and $M$ be an $R$-module. A submodule $N$ of $M$ is called a d-submodule $($resp., an fd-submodule$)$ if $\ann_R(m)\subseteq \ann_R(m')$ $($resp., $\ann_R(F)\subseteq \ann_R(m'))$ for some $m\in N$ $($resp., finite subset $F\subseteq N)$ and $m'\in M$ implies that $m'\in N.$ Many examples, characterizations, and properties of these submodules are given. Moreover, we use them to characterize modules satisfying Property T, reduced modules, and von Neumann regular modules.

Keywords

Baer submodule, d-submodule, fd-submodule, 0-submodule, annihilator

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