Baer submodules of modules over commutative rings

Anahtar Kelimeler:

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

Baer submodules of modules over commutative rings

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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