Geodesic
Zero-divisor Graphs of Ore Extensions Over Reversible Rings
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 794-805

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DOI

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.
DOI : 10.4153/CMB-2016-039-2
Mots-clés : 13B25, 05C12, 16S36, zero-divisor graphs, reversible rings, McCoy rings, polynomial rings, power series rings 
Hashemi, E.; Amirjan, R. Zero-divisor Graphs of Ore Extensions Over Reversible Rings. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 794-805. doi: 10.4153/CMB-2016-039-2
@article{10_4153_CMB_2016_039_2,
     author = {Hashemi, E. and Amirjan, R.},
     title = {Zero-divisor {Graphs} of {Ore} {Extensions} {Over} {Reversible} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {794--805},
     year = {2016},
     volume = {59},
     number = {4},
     doi = {10.4153/CMB-2016-039-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-039-2/}
}
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