Zariski Topologies on Graded Ideals

Malik Bataineh; Azzh Saad Alshehry; Rashid Abu-Dawwas

doi:10.2478/tmmp-2021-0015

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Zariski Topologies on Graded Ideals

Tatra Mountains Mathematical Publications

Volume 78 (2021): Issue 1 (October 2021)

By: Malik Bataineh, Azzh Saad Alshehry and Rashid Abu-Dawwas

Open Access

|Jan 2022

Abstract

In this paper, we show there are strong relations between the algebraic properties of a graded commutative ring R and topological properties of open subsets of Zariski topology on the graded prime spectrum of R. We examine some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense, and irreducible. We also present a characterization for the radical of a graded ideal in R by using topological properties.

References

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0015 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 215 - 224

Submitted on: Jun 7, 2020

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

graded prime ideal,

graded radical ideal,

Zariski topology

Related subjects:

Mathematics,

General mathematics

© 2022 Malik Bataineh, Azzh Saad Alshehry, Rashid Abu-Dawwas, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 78 (2021): Issue 1 (October 2021)