ON S-2-ABSORBING PRIMARY SUBMODULES

Abstract

This article introduces the concept of $S$-2-absorbing primary submodule as a generalization of 2-absorbing primary submodule. Let $S$ be a multiplicatively closed subset of a ring $R$ and $M$ an $R$-module. A proper submodule $N$ of $M$ is said to be an  $S$-2-absorbing primary submodule of $M$ if $(N :_{R} M)\cap S = \phi$ and there exists a fixed element $s\in S$ such that whenever $abm \in N$ for some $a, b \in R$ and $m\in M$, then either $sam \in N$ or $sbm \in N$ or $sab \in \sqrt{(N :_{R} M)}$. We give several examples, properties and characterizations related to the concept. Moreover, we investigate the conditions that force a submodule to be $S$-2-absorbing primary.