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arXiv · 1203.5939

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

Yu. N. Maltsev·E. V. Zhuravlev·A. S. Kuzmina
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Abstract

The zero-divisor graph $Γ(R)$ of an associative ring $R$ is the 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 iff either $xy=0$ or $yx=0$. In the present paper, we give a full description of ring varieties where every finite ring is uniquely determined by its zero-divisor graph.

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Yu. N. Maltsev, E. V. Zhuravlev, A. S. Kuzmina. 2012-03-27. Full Descripion of ring varieties whose finite rings are uniquely determined by their zero-divisor graphs. https://arxiv.org/abs/1203.5939

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