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The description of varieties of rings whose finite rings are uniquely determined by their zero-divisor graphs

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Abstract

The zero-divisor graph of an associative ring R is defined as follows. The vertices of the graph are all the nonzero elements of the ring. Two different vertices x and y of the graph are connected by an edge if and only if xy = 0 or yx = 0.

In this paper, we give the complete description of varieties of associative rings all of whose finite rings are uniquely determined by their zero-divisor graphs.

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Author information

Authors and Affiliations

  1. Altai State University, ul. Lenina 61, Barnaul, 656049, Russia

    E. V. Zhuravlev

  2. Altai State Pedagogical Academy, ul. Molodezhnaya 55, Barnaul, 656031, Russia

    A. S. Kuz’mina & Yu. N. Mal’tsev

Authors
  1. E. V. Zhuravlev
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  2. A. S. Kuz’mina
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  3. Yu. N. Mal’tsev
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Corresponding author

Correspondence to E. V. Zhuravlev.

Additional information

Original Russian Text © E.V. Zhuravlev, A.S. Kuz’mina, and Yu.N. Mal’tsev, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 6, pp. 13–24.

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Zhuravlev, E.V., Kuz’mina, A.S. & Mal’tsev, Y.N. The description of varieties of rings whose finite rings are uniquely determined by their zero-divisor graphs. Russ Math. 57, 10–20 (2013). https://doi.org/10.3103/S1066369X13060029

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  • DOI: https://doi.org/10.3103/S1066369X13060029

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