Group Action on the Set of Nonunits in Rings

Eman S. Almotairi, M. Imran Bhat, Ahmad M. Alghamdi and Niansheng Tang

Journal of Mathematics, 2023, vol. 2023, 1-4

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9711759

DOI: 10.1155/2023/9711759

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