Geodesic
On some properties of ring varieties, where isomorphic zero-divisor graphs of finite rings give isomorhic rings
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 179-190.

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Denote by $\Gamma(R)$ the zero-divisor graph of an associative ring $R$. In this paper, we study varieties of associative rings, where an isomorphism of $\Gamma(R)$ and $\Gamma(S)$ implies an isomorphism of the rings $R$ and $S$ for any finite rings $R$, $S$.
Keywords: zero-divisor graph, variety of associative rings, finite ring. 
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A. S. Kuz'mina. On some properties of ring varieties, where isomorphic zero-divisor graphs of finite rings give  isomorhic rings. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 179-190. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a15/

[1] Akbari S., Mohammadian A., “On the zero-divisor graph of a commutative ring”, Journal of Algebra, 274 (2004), 847–855 | DOI | MR | Zbl

[2] Akbari S., Mohammadian A., “On zero-divisor graphs of finite rings”, Journal of Algebra, 314 (2007), 168–184 | DOI | MR | Zbl

[3] Anderson D.F., Livingston P.S., “The Zero-Divisor Graph of a Commutative Ring”, Journal of Algebra, 217 (1999), 434–447 | DOI | MR | Zbl

[4] Beck I., “Coloring of Commutative Rings”, Journal of Algebra, 116 (1988), 208–226 | DOI | MR | Zbl

[5] Redmond S.P., “The zero-divisor graph of a noncommutative ring”, Int. J. Commut. rings, 1:4 (2002), 203–211

[6] Rowen L.H., Polynomial Identities in Ring Theory, Academic Press, 1980 | MR | Zbl

[7] Tarski A., “Equationally complete rings and relation algebras”, Indag. Math., 18 (1956), 39–46 | MR

[8] Andrunakievich V.A., Ryabukhin Yu.M., Radikaly algebr i strukturnaya teoriya, Nauka, Moskva, 1979 | MR

[9] Dzhekobson N., Stroenie kolets, Izd-vo inostr. literatury, Moskva, 1961 | MR

[10] Elizarov V.P., Konechnye koltsa, Gelios ARV, Moskva, 2006

[11] Kuzmina A.S., “Opisanie konechnykh nenilpotentnykh kolets, imeyuschikh planarnye grafy delitelei nulya”, Diskretnaya matematika, 21:4 (2009), 60–75 | MR

[12] Lvov I.V., “O mnogoobraziya assotsiativnykh kolets I”, Algebra i logika, 12:3 (1973), 269–297 | MR