Geodesic
Description of ring varieties whose finite rings are uniquely determined by their zero-divisor graphs
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 13-24.

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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. 
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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. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 13-24. http://geodesic.mathdoc.fr/item/IVM_2013_6_a1/

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