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The Zariski topology on the graded primary spectrum over graded commutative rings

In: Tatra Mountains Mathematical Publications, vol. 74, no. 2
Khaldoun Al-Zoubi - Malik Jaradat

Details:

Year, pages: 2019, 7 - 16
Language: eng
Keywords:
Zariski topology, graded primary spectrum, graded primary ideals.
Article type: mathematics
Document type: Scientific article *.pdf
About article:
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 \textit{a graded primary ideal} if whenever $rgsh\in P$, we have $rg\in P$ or $sh\in Gr(P)$, where $rg,sg\in h(R).$ The \textit{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.
How to cite:
ISO 690:
Al-Zoubi, K., Jaradat, M. 2019. The Zariski topology on the graded primary spectrum over graded commutative rings. In Tatra Mountains Mathematical Publications, vol. 74, no.2, pp. 7-16. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0015

APA:
Al-Zoubi, K., Jaradat, M. (2019). The Zariski topology on the graded primary spectrum over graded commutative rings. Tatra Mountains Mathematical Publications, 74(2), 7-16. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0015
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 25. 10. 2019
Rights:
Licensed under the Creative Commons Attribution-NC-ND4.0 International Public License.