On varieties of rings whose finite rings are determined by their zero-divisor graphs

Details On varieties of rings whose finite rings are determined by their zero-divisor graphs On varieties of rings whose finite rings are determined by their zero-divisor graphs

2012-01-17

arxiv.org/abs/1201.3441v1

Mathematics

Rings and Algebras

8 pages, to appear in Asian-European Journal of Mathematics

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 study some properties of ring varieties where every finite ring is uniquely determined by its zero-divisor graph.

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