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The News of Altai State University
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1(61)2009
Mathematics and Mechanics

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A.S. Kuz#mina

On Stucture of Rings with Planar Zero-Divisor Graphs

The zero-divisor graph of an associative ring R is the graph whose vertices are nonzero (one-sided and two-sided) zero-divisors of R, and two distinct vertices x and y are joined by an edge if xy = 0 or yx = 0.
In this paper, we study subdirectly irreducible finite rings that satisfy the identities x2 = x3f(x), ptx = 0, where f(x)∈Z[x] and p is an odd prime number, and have planar zero-divisor graphs.
Keywords: zero-divisor graph, planar graph, Eulerian graph, finite ring, rings with polynomial identities.

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