On graded $A$-2-absorbing submodules of graded modules over graded commutative rings

TL;DR

This paper introduces and studies graded A-2-absorbing submodules of graded modules over graded commutative rings, generalizing existing concepts and exploring their properties.

Contribution

It defines the new concept of graded A-2-absorbing submodules and investigates their properties, extending the theory of graded submodules.

Findings

Introduction of graded A-2-absorbing submodules

Generalization of graded 2-absorbing and A-prime submodules

Analysis of properties of these new submodules

Abstract

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring, $M$ a graded $R$-module and $A\subseteq h(R)$ a multiplicatively closed subset of $R$. In this paper, we introduce the concept of graded $A$-2-absorbing submodules of $M$ as a generalization of graded 2-absorbing submodules and graded $A$-prime submodules of $M.$ We investigate some properties of this class of graded submodules.