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

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

2012-03-27

arxiv.org/abs/1203.5939v1

Mathematics

Rings and Algebras

15 pages, in Russian

Scientific paper

The zero-divisor graph $\Gamma(R)$ 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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