On Graded Classical S-Primary Submodules

TL;DR

This paper introduces graded classical S-primary submodules, extending the concept of graded classical primary submodules, and explores their properties and characteristics within module theory.

Contribution

It defines and studies the properties of graded classical S-primary submodules, extending existing concepts in graded module theory.

Findings

Characterization of graded classical S-primary submodules

Conditions under which submodules are S-primary

Properties and examples of these submodules

Abstract

The purpose of this article is to introduce the graded classical S-primary submodules which are extensions of graded classical primary submodules. We state that P is a graded classical S-primary submodule of R-module M if there exists $s\in S$ such that $x,y \in h(R)$ and $m \in h(M)$, if $xym \in P$, then $sxm \in P$ or $sy^nm \in P$ for some positive integer n. Several properties and characteristics of graded classical S-primary submodules have been studied.