Abstract

Let $\Omega$ be a group with identity $e$, $\Gamma$ be a $\Omega$-graded commutative ring and $\Im$ a graded $\Gamma$-module. In this article, we introduce the concept of $gr$-$C$-$2^{A}$-secondary submodules and investigate some properties of this new class of graded submodules. A non-zero graded submodule $S$ of $\Im$ is said to be a $gr$-$C$-$2^{A}$-secondary submodule if whenever $r,s \in h(\Gamma)$, $L$ is a graded submodule of $\Im$, and $rs\,S\subseteq L$, then either $r\,S\subseteq L$ or $s\,S \subseteq L$ or $rs \in Gr(Ann_\Gamma(S))$.

Keywords: Graded classical 2-absorbing secondary submodules; graded 2-absorbing submodules; graded 2-absorbing primary submodules.

MSC: 13A02, 16W50

DOI: 10.57016/MV-HGLA1043

Pages:  1--7