Baer submodules of modules over commutative rings

Yıl 2023, Cilt: 34 Sayı: 34, 31 - 47, 10.07.2023

Adam Anebrı Hwankoo Kım Najib Mahdou

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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