<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we show there are strong relations between the algebraic properties of a graded commutative ring <italic>R</italic> and topological properties of open subsets of Zariski topology on the graded prime spectrum of <italic>R</italic>. 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 <italic>R</italic> by using topological properties.</p>
</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.

Zariski Topologies on Graded Ideals

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Zariski Topologies on Graded Ideals"}

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 Topologies on Graded Ideals

Published Online: Jan 01, 2022

Page range: 215 - 224

Received: Jun 07, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0015

Keywords
graded prime ideal, graded radical ideal, Zariski topology

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Zariski Topologies on Graded Ideals

Published Online: Jan 01, 2022

Page range: 215 - 224

Received: Jun 07, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0015

Keywordsgraded prime ideal, graded radical ideal, Zariski topology

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
graded prime ideal, graded radical ideal, Zariski topology