Scientific journal "The News of Altai State University". 2009 #1(61). Mathematics and Mechanics.

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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), p^tx = 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.

Full text at PDF, 235Kb. Language: russian.

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