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 *x*^{2} = *x*^{3}*f*(*x*), *p*^{t}x = 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.