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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 6, Pages 13–24 (Mi ivm8801)  
This article is cited in 7 scientific papers (total in 7 papers)

Description of ring varieties whose finite rings are uniquely determined by their zero-divisor graphs

E. V. Zhuravleva, A. S. Kuz'minab, Yu. N. Mal'tsevb

a Chair of Algebra and Mathematical Logic, Altai State University, Barnaul, Russia
b Chair of Algebra and Mathematics Teaching Principles, Altai State Pedagogical Academy, Barnaul, Russia
Full-text PDF (243 kB) Citations (7)
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Abstract: The zero-divisor graph $\Gamma(R)$ of an associative ring $R$ is a graph whose vertices are all nonzero zero-divisors (one-sided and two-sided) of $R$, and two distinct vertices $x$ and $y$ are joined by an edge if and only if either $xy=0$ or $yx=0$.
In the present paper, we give a full description of ring varieties whose finite rings are uniquely determined by their zero-divisor graphs.
Keywords: zero-divisor graph, finite ring, variety of associative rings.
Received: 24.03.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 6, Pages 10–20
DOI: https://doi.org/10.3103/S1066369X13060029
Bibliographic databases:
Document Type: Article
UDC: 512.552
Language: Russian
Citation: E. V. Zhuravlev, A. S. Kuz'mina, Yu. N. Mal'tsev, “Description of ring varieties whose finite rings are uniquely determined by their zero-divisor graphs”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 6, 13–24; Russian Math. (Iz. VUZ), 57:6 (2013), 10–20
Citation in format AMSBIB
\Bibitem{ZhuKuzMal13}
\by E.~V.~Zhuravlev, A.~S.~Kuz'mina, Yu.~N.~Mal'tsev
\paper Description of ring varieties whose finite rings are uniquely determined by their zero-divisor graphs
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 6
\pages 13--24
\mathnet{http://mi.mathnet.ru/ivm8801}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 6
\pages 10--20
\crossref{https://doi.org/10.3103/S1066369X13060029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878803673}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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