Zero-divisor Graphs of Ore Extensions over Reversible Rings
Printed: Dec 2016
Let $R$ 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 $R[[x;\alpha]]$, whenever $R$ is reversible and $\alpha$-compatible. Moreover, we compare the diameter and girth of the zero-divisor
graphs of $\Gamma(R)$, $\Gamma(R[x;\alpha,\delta])$ and $\Gamma(R[[x;\alpha]])$,
$R$ is reversible and $(\alpha,\delta)$-compatible.
zero-divisor graphs, reversible rings, McCoy rings, polynomial rings, power series rings
13B25 - Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]
05C12 - Distance in graphs
16S36 - Ordinary and skew polynomial rings and semigroup rings [See also 20M25]