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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 2, Pages 281–291
DOI: https://doi.org/10.33048/smzh.2023.64.204
(Mi smj7761)
 

Compressed and partially compressed zero-divisor graphs of finite associative rings

A. A. Afanas'eva, A. S. Monastyrevab

a Novosibirsk State University
b Altai State University, Barnaul
References:
Abstract: We study some properties of the compressed zero-divisor graph of a finite ring and the partially compressed zero-divisor graph of a finite nilpotent ring. In particular, we describe all nilpotent finite rings whose compressed zero-divisor graphs are some complete graphs with loops. Furthermore, we introduce the notion of partially compressed zero-divisor graph for the nilpotent rings and study the properties of the group. Also, we describe the finite rings whose compressed zero-divisor graph contains a bridge.
Keywords: finite ring, zero-divisor, nilpotent ring, compressed zero-divisor graph, partially compressed zero-divisor graph.
Received: 14.07.2022
Revised: 22.07.2022
Accepted: 15.08.2022
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 2, Pages 291–299
DOI: https://doi.org/10.1134/S0037446623020040
Bibliographic databases:
Document Type: Article
UDC: 512.55
Language: Russian
Citation: A. A. Afanas'ev, A. S. Monastyreva, “Compressed and partially compressed zero-divisor graphs of finite associative rings”, Sibirsk. Mat. Zh., 64:2 (2023), 281–291; Siberian Math. J., 64:2 (2023), 291–299
Citation in format AMSBIB
\Bibitem{AfaMon23}
\by A.~A.~Afanas'ev, A.~S.~Monastyreva
\paper Compressed and partially compressed zero-divisor graphs of finite associative rings
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 2
\pages 281--291
\mathnet{http://mi.mathnet.ru/smj7761}
\crossref{https://doi.org/10.33048/smzh.2023.64.204}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4567664}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 2
\pages 291--299
\crossref{https://doi.org/10.1134/S0037446623020040}
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