ON GRADED 2-ABSORBING COPRIMARY SUBMODULES

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 nonzero 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 $\left(K\hspace{0.17em}{:}_R\hspace{0.17em}N\right)$ or $xy\in An{n}_R\left(N\right)$. Several results have been achieved.