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Algebra Logika, 2013, Volume 52, Number 2, Pages 203–218 (Mi al582)  

This article is cited in 2 scientific papers (total in 2 papers)

Describing ring varieties in which all finite rings have Hamiltonian zero-divisor graphs

Yu. N. Mal'tsev, A. S. Kuz'mina

Altai State Pedagogical Academy, Barnaul, Russia

Abstract: The zero-divisor graph of an associative ring $R$ is a graph such that its vertices are all nonzero (one-sided and two-sided) zero-divisors, and moreover, two distinct vertices $x$ and $y$ are joined by an edge iff $xy=0$ or $yx=0$. We give a complete description of varieties of associative rings in which all finite rings have Hamiltonian zero-divisor graphs. Also finite decomposable rings with unity having Hamiltonian zero-divisor graphs are characterized.

Keywords: zero-divisor graph, Hamiltonian graph, variety of associative rings, finite ring.

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English version:
Algebra and Logic, 2013, 52:2, 137–146

Bibliographic databases:

Document Type: Article
UDC: 512.552.4
Received: 09.01.2013
Revised: 22.02.2013

Citation: Yu. N. Mal'tsev, A. S. Kuz'mina, “Describing ring varieties in which all finite rings have Hamiltonian zero-divisor graphs”, Algebra Logika, 52:2 (2013), 203–218; Algebra and Logic, 52:2 (2013), 137–146

Citation in format AMSBIB
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\by Yu.~N.~Mal'tsev, A.~S.~Kuz'mina
\paper Describing ring varieties in which all finite rings have Hamiltonian zero-divisor graphs
\jour Algebra Logika
\yr 2013
\vol 52
\issue 2
\pages 203--218
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\jour Algebra and Logic
\yr 2013
\vol 52
\issue 2
\pages 137--146
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Kuzmina, Yu. N. Maltsev, “Finite rings with some restrictions on zero-divisor graphs”, Russian Math. (Iz. VUZ), 58:12 (2014), 41–50  mathnet  crossref
    2. A. S. Kuzmina, “O stroenii konechnykh nilpotentnykh kolets s ogranicheniyami na grafy delitelei nulya”, Sib. elektron. matem. izv., 12 (2015), 122–129  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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