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Zero-divisor Graphs of Ore Extensions over Reversible Rings

Published:2016-07-18
Printed: Dec 2016
• Ebrahim Hashemi,
Department of Mathematics, Shahrood University of Technology, , P.O.~Box: 316-3619995161, Shahrood, Iran
• R. Amirjan,
Department of Mathematics, Shahrood University of Technology, , P.O.~Box: 316-3619995161, Shahrood, Iran
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Abstract

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 $\Gamma(R[[x;\alpha]])$, when $R$ is reversible and $(\alpha,\delta)$-compatible.
 Keywords: zero-divisor graphs, reversible rings, McCoy rings, polynomial rings, power series rings
 MSC Classifications: 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]

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