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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |