ZERO-DIVISOR GRAPHS OF ÖRE EXTENSION RINGS

Abstract

Let R be an associative ring with two-sided multiplicative identity. In this paper, in the case that R is a commutative α-compatible ring, we compare the diameter (and girth) of the zero-divisor graphs Γ(R) and Γ(R[x;α, δ]). Moreover, we study the zero-divisors of the Öre extension ring R[x;α, δ], whenever R is reversible and (α, δ)-compatible.