Baer submodules of modules over commutative rings

Authors : Adam ANEBRI, Hwankoo KIM, Najib MAHDOU

Pages : 31-47

Doi:10.24330/ieja.1252741

View : 49 | Download : 107

Publication Date : 2023-07-10

Article Type : Research Paper

Abstract :Let $R$ be a commutative ring and $M$ be an $R$-module. A submodule $N$ of $M$ is called a d-submodule $insert ignore into journalissuearticles values($resp., an fd-submodule$);$ if $\\ann_Rinsert ignore into journalissuearticles values(m);\\subseteq \\ann_Rinsert ignore into journalissuearticles values(m\`);$ $insert ignore into journalissuearticles values($resp., $\\ann_Rinsert ignore into journalissuearticles values(F);\\subseteq \\ann_Rinsert ignore into journalissuearticles values(m\`););$ for some $m\\in N$ $insert ignore into journalissuearticles values($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