On Graded classical 2-absorbing second submodules of graded modules over graded commutative rings

TL;DR

This paper introduces and studies new classes of graded submodules called graded classical and strongly classical 2-absorbing second submodules over graded commutative rings, providing foundational results about their properties.

Contribution

It defines the concepts of graded classical and strongly classical 2-absorbing second submodules and explores their properties within graded modules over graded commutative rings.

Findings

Characterization of graded classical 2-absorbing second submodules

Properties of homogeneous components of these submodules

Results connecting these classes to existing submodule concepts

Abstract

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded classical and graded strongly classical 2-absorbing second submodules of graded modules over a graded commutative rings. A number of results concerning these classes of graded submodules and their homogeneous components are given.