On varieties of rings whose finite rings are determined by their zero-divisor graphs
Abstract
The zero-divisor graph (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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