The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring

Let R be a G-graded ring and M be a G-graded R-module. We define the graded primary spectrum of M, denoted by PSG(M), to be the set of all graded primary submodules Q of M such that (GrM(Q) :RM) = Gr((Q:RM)). In this paper, we define a topology on PSG(M) having the Zariski topology on the graded pri...

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Bibliographic Details
Published in:Applied General Topology
Main Authors: Saif Salam, Khaldoun Al-Zoubi
Format: Article
Language:English
Published: Universitat Politècnica de València 2022-10-01
Subjects:
graded primary submodules
graded primary spectrum
zariski topology
Online Access:https://polipapers.upv.es/index.php/AGT/article/view/16332
Description
Summary:Let R be a G-graded ring and M be a G-graded R-module. We define the graded primary spectrum of M, denoted by PSG(M), to be the set of all graded primary submodules Q of M such that (GrM(Q) :RM) = Gr((Q:RM)). In this paper, we define a topology on PSG(M) having the Zariski topology on the graded prime spectrum SpecG(M) as a subspace topology, and investigate several topological properties of this topological space.
ISSN:1576-9402
1989-4147

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