<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>G</italic> be a group with identity <italic>e</italic> and let <italic>R</italic> be a <italic>G</italic>-graded ring. A proper graded ideal <italic>P</italic> of <italic>R</italic> is called <italic>a graded primary ideal</italic> if whenever <italic>rgsh∈P</italic>, we have <italic>rg∈ P</italic> or <italic>sh∈ Gr</italic>(<italic>P</italic>), where <italic>rg,sg∈ h</italic>(<italic>R</italic>). The <italic>graded primary spectrum p.Specg</italic>(<italic>R</italic>) is defined to be the set of all graded primary ideals of <italic>R</italic>.In this paper, we define a topology on <italic>p.Specg</italic>(<italic>R</italic>), called Zariski topology, which is analogous to that for <italic>Specg</italic>(<italic>R</italic>), and investigate several properties of the topology.</abstract>

Let G be a group with identity e and let R be a G-graded ring. A proper graded ideal P of R is called a graded primary ideal if whenever rgsh∈P, we have rg∈ P or sh∈ Gr(P), where rg,sg∈ h(R). The graded primary spectrum p.Specg(R) is defined to be the set of all graded primary ideals of R.In this paper, we define a topology on p.Specg(R), called Zariski topology, which is analogous to that for Specg(R), and investigate several properties of the topology.

The Zariski Topology on the Graded Primary Spectrum Over Graded Commutative Rings

Jordan University of Science and Technology

Department of Mathematics, The international School of Choueifat (MHS-AlDaid)

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Let G be a group with identity e and let R be a G-graded ring. A proper graded ideal P of R is called a graded primary ideal if whenever rgsh∈P, we have rg∈ P...

The Zariski Topology on the Graded Primary Spectrum Over Graded Commutative Rings

Published Online: Nov 15, 2019

Page range: 7 - 16

Received: Feb 28, 2019

DOI: https://doi.org/10.2478/tmmp-2019-0015

Keywords
Zariski topology, graded primary spectrum, graded primary ideals

© 2019 Khaldoun Al-Zoubi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Zariski Topology on the Graded Primary Spectrum Over Graded Commutative Rings

Published Online: Nov 15, 2019

Page range: 7 - 16

Received: Feb 28, 2019

DOI: https://doi.org/10.2478/tmmp-2019-0015

KeywordsZariski topology, graded primary spectrum, graded primary ideals

© 2019 Khaldoun Al-Zoubi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Zariski topology, graded primary spectrum, graded primary ideals