Graded Pseudo Weakly Prime Spectrum Of Graded Topological Modules

TL;DR

This paper introduces graded pseudo weakly prime submodules in G-graded modules, explores their spectral topology, and links topological properties to algebraic structures, extending the concept of prime ideals.

Contribution

It defines and studies graded pseudo weakly prime submodules and their spectra, extending the theory of prime ideals in graded modules.

Findings

The graded pseudo weakly prime spectrum is equipped with a Zariski topology.

Topological properties are connected to algebraic properties of G-graded modules.

The study extends the understanding of prime spectra in the context of graded modules.

Abstract

In this study, we introduce graded pseudo weakly prime submodules of G-graded R-modules, which are an extension of graded weakly prime ideals over G-graded rings. On the graded spectrum of graded pseudo weakly prime submodules, we investigate the Zariski topology. Different aspects of this topological space are investigated, and they are linked to the algebraic properties of the G-graded R-modules under study.