Zero-divisor Graphs of Ore Extensions Over Reversible Rings. Issue 4 (1st December 2016)

• Record Type: Journal Article
• Authors: Hashemi, E.; Amirjan, R.
• Is Part Of: Canadian mathematical bulletin =. Volume 59:Issue 4(2016)
• Page Start: 794
• Page End: 805
• Publication Date: 2016-12-01
• Subjects: 13B25 -- 05C12 -- 16S36; zero-divisor graphs -- reversible rings -- McCoy rings -- polynomial rings -- power series rings; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2016-039-2
• Languages: English
• ISSNs: 0008-4395

Abstract

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 $R\left[\!\left[ x;\, \alpha \right]\!\right]$, 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.