Bulletin of the
Korean Mathematical Society BKMS

We, in this paper, study the commutativity of skew polynomials at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of strongly skew reversibility. A ring $R$ is be said to be \emph{strongly $\alpha$-skew reversible} if the skew polynomial ring $R[x;\alpha]$ is reversible. We examine some characterizations and extensions of strongly $\alpha$-skew reversible rings in relation with several ring theoretic properties which have roles in ring theory.

Keywords: strongly $\alpha$-skew reversible ring, reversible ring, $\alpha$-rigid ring, skew polynomial ring, Dorroh extension

MSC numbers: Primary 16W20, 16U80; Secondary 16S36