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

Saif Salam; Khaldoun Al-Zoubi

doi:10.4995/agt.2022.16332

Authors

Saif Salam Jordan University of Science and Technology https://orcid.org/0000-0002-1330-2556
Khaldoun Al-Zoubi Jordan University of Science and Technology https://orcid.org/0000-0001-6082-4480

DOI:

https://doi.org/10.4995/agt.2022.16332

Keywords:

graded primary submodules, graded primary spectrum, Zariski topology

Abstract

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.

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Author Biographies

Saif Salam, Jordan University of Science and Technology

Department of Mathematics and Statistics

Khaldoun Al-Zoubi, Jordan University of Science and Technology

Department of Mathematics and Statistics

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