Group Action on the Set of Nonunits in Rings
Let R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x. We also investigate the question on zero-divisor graphs posed in the literature such that when t...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/9711759 |
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| author | Eman S. Almotairi M. Imran Bhat Ahmad M. Alghamdi |
| author_facet | Eman S. Almotairi M. Imran Bhat Ahmad M. Alghamdi |
| author_sort | Eman S. Almotairi |
| collection | DOAJ |
| description | Let R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x. We also investigate the question on zero-divisor graphs posed in the literature such that when the equality o1−e=ave holds in a commutative regular ring R with identity. Here, e is a nonzero idempotent of R which is not the identity element of R. |
| format | Article |
| id | doaj-art-9d555432a39045cbb446d0c34678b66b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9d555432a39045cbb446d0c34678b66b2025-02-03T06:42:47ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/9711759Group Action on the Set of Nonunits in RingsEman S. Almotairi0M. Imran Bhat1Ahmad M. Alghamdi2Mathematics DepartmentDepartment of MathematicsMathematics DepartmentLet R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x. We also investigate the question on zero-divisor graphs posed in the literature such that when the equality o1−e=ave holds in a commutative regular ring R with identity. Here, e is a nonzero idempotent of R which is not the identity element of R.http://dx.doi.org/10.1155/2023/9711759 |
| spellingShingle | Eman S. Almotairi M. Imran Bhat Ahmad M. Alghamdi Group Action on the Set of Nonunits in Rings Journal of Mathematics |
| title | Group Action on the Set of Nonunits in Rings |
| title_full | Group Action on the Set of Nonunits in Rings |
| title_fullStr | Group Action on the Set of Nonunits in Rings |
| title_full_unstemmed | Group Action on the Set of Nonunits in Rings |
| title_short | Group Action on the Set of Nonunits in Rings |
| title_sort | group action on the set of nonunits in rings |
| url | http://dx.doi.org/10.1155/2023/9711759 |
| work_keys_str_mv | AT emansalmotairi groupactiononthesetofnonunitsinrings AT mimranbhat groupactiononthesetofnonunitsinrings AT ahmadmalghamdi groupactiononthesetofnonunitsinrings |