On Graded 2-Absorbing Coprimary Submodules

TL;DR

This paper introduces and explores the properties of graded 2-absorbing coprimary submodules, a new generalization in the theory of graded modules, extending previous concepts like strongly 2-absorbing second submodules.

Contribution

It defines graded 2-absorbing coprimary submodules and investigates their properties, broadening the understanding of submodule structures in graded modules.

Findings

Established the definition of graded 2-absorbing coprimary submodules.

Derived properties and characterizations of these submodules.

Connected the new concept with existing notions like graded radicals and annihilators.

Abstract

The aim of this article is to introduce the concept of graded $2$-absorbing coprimary submodules as a generalization of graded strongly $2$-absorbing second submodules, and explore some properties of this class. A non-zero graded $R$-submodule $N$ of a graded $R$-module $M$ is called a graded $2$-absorbing coprimary $R$-submodule if whenever $x, y$ are homogeneous elements of $R$ and $K$ is a graded $R$-submodule of $M$ such that $xyN\subseteq K$, then either $x$ or $y$ is in the graded radical of $(K :_{R} N)$ or $xy\in Ann_{R}(N)$. Several results have been achieved.