Zero-divisor Graphs of Ore Extensions Over Reversible Rings. Issue 4 (1st December 2016) - Hashemi, E.; Amirjan, R.
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.