$S$-2-absorbing submodules and $S$-2-absorbing second submodules

TL;DR

This paper introduces and explores the concept of S-2-absorbing second submodules in modules over commutative rings, generalizing existing notions and analyzing their properties and related submodules.

Contribution

It defines S-2-absorbing second submodules, extending previous concepts, and investigates their properties and relationships within module theory.

Findings

Characterization of S-2-absorbing second submodules

Relations between S-2-absorbing and other submodule classes

Properties and conditions for S-2-absorbing submodules

Abstract

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. In this paper, we introduce the notion of S-2-absorbing second submodules of M as a generalization of S-second submodules and strongly 2-absorbing second submodules of M. We investigate some properties of this class of submodules. Also, we obtain some results concerning S-2-absorbing submodules of M.