Zero-divisor graphs of twisted partial skew generalized power series rings
Purpose – The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring RG,≤;Θ and the corresponding structure of its zero-divisor graph Γ̅RG,≤;Θ. Design/methodology/approach – The authors first introduce the history and...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2022-06-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-10-2021-0253/full/pdf |
| _version_ | 1797791657752526848 |
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| author | Mohammed H. Fahmy Ahmed Ageeb Elokl Ramy Abdel-Khalek |
| author_facet | Mohammed H. Fahmy Ahmed Ageeb Elokl Ramy Abdel-Khalek |
| author_sort | Mohammed H. Fahmy |
| collection | DOAJ |
| description | Purpose – The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring RG,≤;Θ and the corresponding structure of its zero-divisor graph Γ̅RG,≤;Θ. Design/methodology/approach – The authors first introduce the history and motivation of this paper. Secondly, the authors give a brief exposition of twisted partial skew generalized power series ring, in addition to presenting some properties of such structure, for instance, a-rigid ring, a-compatible ring and (G,a)-McCoy ring. Finally, the study’s main results are stated and proved. Findings – The authors establish the relation between the diameter and girth of the zero-divisor graph of twisted partial skew generalized power series ring RG,≤;Θ and the zero-divisor graph of the ground ring R. The authors also provide counterexamples to demonstrate that some conditions of the results are not redundant. As well the authors indicate that some conditions of recent results can be omitted. Originality/value – The results of the twisted partial skew generalized power series ring embrace a wide range of results of classical ring theoretic extensions, including Laurent (skew Laurent) polynomial ring, Laurent (skew Laurent) power series ring and group (skew group) ring and of course their partial skew versions. |
| first_indexed | 2024-03-13T02:21:58Z |
| format | Article |
| id | doaj.art-60cf952367ab4d829c3a34bca94579f7 |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:21:58Z |
| publishDate | 2022-06-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-60cf952367ab4d829c3a34bca94579f72023-06-30T09:18:57ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142022-06-0128224325210.1108/AJMS-10-2021-0253Zero-divisor graphs of twisted partial skew generalized power series ringsMohammed H. Fahmy0Ahmed Ageeb Elokl1Ramy Abdel-Khalek2Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, EgyptDepartment of Mathematics, Faculty of Science, Al-Azhar University, Cairo, EgyptDepartment of Mathematics, Faculty of Science, Al-Azhar University, Cairo, EgyptPurpose – The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring RG,≤;Θ and the corresponding structure of its zero-divisor graph Γ̅RG,≤;Θ. Design/methodology/approach – The authors first introduce the history and motivation of this paper. Secondly, the authors give a brief exposition of twisted partial skew generalized power series ring, in addition to presenting some properties of such structure, for instance, a-rigid ring, a-compatible ring and (G,a)-McCoy ring. Finally, the study’s main results are stated and proved. Findings – The authors establish the relation between the diameter and girth of the zero-divisor graph of twisted partial skew generalized power series ring RG,≤;Θ and the zero-divisor graph of the ground ring R. The authors also provide counterexamples to demonstrate that some conditions of the results are not redundant. As well the authors indicate that some conditions of recent results can be omitted. Originality/value – The results of the twisted partial skew generalized power series ring embrace a wide range of results of classical ring theoretic extensions, including Laurent (skew Laurent) polynomial ring, Laurent (skew Laurent) power series ring and group (skew group) ring and of course their partial skew versions.https://www.emerald.com/insight/content/doi/10.1108/AJMS-10-2021-0253/full/pdfTwisted partial skew generalized power series ringZero-divisor graphDiameterGirth |
| spellingShingle | Mohammed H. Fahmy Ahmed Ageeb Elokl Ramy Abdel-Khalek Zero-divisor graphs of twisted partial skew generalized power series rings Arab Journal of Mathematical Sciences Twisted partial skew generalized power series ring Zero-divisor graph Diameter Girth |
| title | Zero-divisor graphs of twisted partial skew generalized power series rings |
| title_full | Zero-divisor graphs of twisted partial skew generalized power series rings |
| title_fullStr | Zero-divisor graphs of twisted partial skew generalized power series rings |
| title_full_unstemmed | Zero-divisor graphs of twisted partial skew generalized power series rings |
| title_short | Zero-divisor graphs of twisted partial skew generalized power series rings |
| title_sort | zero divisor graphs of twisted partial skew generalized power series rings |
| topic | Twisted partial skew generalized power series ring Zero-divisor graph Diameter Girth |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-10-2021-0253/full/pdf |
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