Some properties of graded generalized 2-absorbing submodules

TL;DR

This paper investigates properties of graded generalized 2-absorbing submodules within graded modules over graded rings, especially focusing on cases where the rings are graded gr-Noetherian, to uncover new structural insights.

Contribution

It introduces new results on the structure of graded generalized 2-absorbing submodules and explores their behavior in graded gr-Noetherian rings, extending existing theory.

Findings

Characterization of graded generalized 2-absorbing submodules

Properties of homogeneous components of these submodules

Additional properties in graded gr-Noetherian rings

Abstract

Let $G$ be an abelian group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous components. Special attention has been paid, when graded rings are graded gr-Noetherian, to find extra properties of these graded submodules.