Graded S-1-absorbing prime submodules in graded multiplication modules

Authors : Farkhondeh FARZALIPOUR, Peyman GHIASVAND

Pages : 62-79

Doi:10.24330/ieja.1081701

View : 15 | Download : 11

Publication Date : 2022-07-16

Article Type : Research Paper

Abstract :Let $G$ be a group with identity $e$. Let $R$ be a commutative $G$-graded ring with non-zero identity, $S\subseteq hinsert ignore into journalissuearticles values(R);$ a multiplicatively closed subset of $R$ and $M$ a graded $R$-module. In this article, we introduce and study the concept of graded $S$-1-absorbing prime submodules. A graded submodule $N$ of $M$ with $insert ignore into journalissuearticles values(N:_{R}M);\cap S=\emptyset$ is said to be graded $S$-1-absorbing prime, if there exists an $s_{g}\in S$ such that whenever $a_{h}b_{h`}m_{k}\in N$, then either $s_{g}a_{h}b_{h`}\in insert ignore into journalissuearticles values(N:_{R}M);$ or $s_{g}m_{k}\in N$ for all non-unit elements $a_{h},b_{h`}\in hinsert ignore into journalissuearticles values(R);$ and all $m_{k}\in hinsert ignore into journalissuearticles values(M);$. Some examples, characterizations and properties of graded $S$-1-absorbing prime submodules are given. Moreover, we give some characterizations of graded $S$-1-absorbing prime submodules in graded multiplicative modules.
Keywords : Graded S 1 absorbing prime ideal, graded S 1 absorbing prime submodule, graded multiplication module