Zero-divisor Graphs of Ore Extensions Over Reversible Rings

Hashemi, E. ; Amirjan, R.

Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 794-805

Résumé

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 $R\left[\!\left[ x;\,\alpha\right]\!\right]$ , whenever $R$ is reversible $\alpha$ -compatible. Moreover, we compare the diameter and girth of the zero-divisor graphs of $\Gamma \left( R \right),\,\Gamma \left( R[x;\,\alpha ,\,\delta ] \right)$ , and $\Gamma \left( R\left[\!\left[ x;\,\alpha\right]\!\right] \right)$ , when $R$ is reversible and $\left( \alpha ,\,\delta\right)$ -compatible.

Détail

DOI : 10.4153/CMB-2016-039-2

Mots-clés : 13B25, 05C12, 16S36, zero-divisor graphs, reversible rings, McCoy rings, polynomial rings, power series rings

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