Zero-divisor Graphs of Ore Extensions Over Reversible Rings

Abstract

AbstractLet R be an associative ring with identity. First we prove some results about zero-divisor graphs of reversible rings. Then we study the zero-divisors of the skew power series ring R[[x; α]], whenever R is reversible α-compatible. Moreover, we compare the diameter and girth of the zero-divisor graphs of Γ(R), Γ(R[x; α, δ]), and Γ(R[[x; α]]), when R is reversible and (α, δ)-compatible.