on graded weakly primal submodules over graded modules

TL;DR

This paper introduces and explores graded weakly primal submodules in G-graded modules, generalizing primal submodules, and investigates their properties and characterizations.

Contribution

It presents the concept of graded weakly primal submodules and provides new characterizations and properties, extending the theory of primal submodules in graded modules.

Findings

Characterization of graded weakly primal submodules

Properties of homogeneous components of these submodules

Extension of primal submodule theory to weakly primal case

Abstract

Let $M$ be G-graded R-module. The idea of a graded weakly primal submodule of $M$, which is a generalization of a graded primal submodule, is introduced and discussed in this paper. Some characteristics and characterizations are assigned to these submodules and their homogeneous components.