Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings
In this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $\ast$-rings. Our investigation revolves around characterizing the diameter of a zero-divisor graph in the context of the direct product $\mathcal{S}_1 \oplus...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2024-12-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4503_89ef51575abaf37aa1fef1f1b14f4b54.pdf |
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| author | Mohd Nazim Nadeem Ur Rehman Shabir Ahmad Mir |
| author_facet | Mohd Nazim Nadeem Ur Rehman Shabir Ahmad Mir |
| author_sort | Mohd Nazim |
| collection | DOAJ |
| description | In this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $\ast$-rings. Our investigation revolves around characterizing the diameter of a zero-divisor graph in the context of the direct product $\mathcal{S}_1 \oplus \mathcal{S}_2$, in relation to the diameters observed in the zero-divisor graphs of the constituent $\ast$-rings $\mathcal{S}_1$ and $\mathcal{S}_2$. |
| format | Article |
| id | doaj-art-a3d257f85aee42189ec13c7c00d944d1 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-a3d257f85aee42189ec13c7c00d944d12025-01-04T19:29:56ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052024-12-01135112010.22103/jmmr.2024.23353.16394503Exploring the properties of the zero-divisor graph of direct product of $\ast$-ringsMohd Nazim0Nadeem Ur Rehman1Shabir Ahmad Mir2School of Computational Sciences, Faculty of Science and Technology, JSPM University, Pune, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaSchool of Computational Sciences, Faculty of Science and Technology, JSPM University, Pune, IndiaIn this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $\ast$-rings. Our investigation revolves around characterizing the diameter of a zero-divisor graph in the context of the direct product $\mathcal{S}_1 \oplus \mathcal{S}_2$, in relation to the diameters observed in the zero-divisor graphs of the constituent $\ast$-rings $\mathcal{S}_1$ and $\mathcal{S}_2$.https://jmmrc.uk.ac.ir/article_4503_89ef51575abaf37aa1fef1f1b14f4b54.pdf$\ast$-ringrickart $\ast$-ringzero-divisor graph |
| spellingShingle | Mohd Nazim Nadeem Ur Rehman Shabir Ahmad Mir Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings Journal of Mahani Mathematical Research $\ast$-ring rickart $\ast$-ring zero-divisor graph |
| title | Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings |
| title_full | Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings |
| title_fullStr | Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings |
| title_full_unstemmed | Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings |
| title_short | Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings |
| title_sort | exploring the properties of the zero divisor graph of direct product of ast rings |
| topic | $\ast$-ring rickart $\ast$-ring zero-divisor graph |
| url | https://jmmrc.uk.ac.ir/article_4503_89ef51575abaf37aa1fef1f1b14f4b54.pdf |
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