Bull. Korean Math. Soc. 2017; 54(1): 51-69
Online first article August 25, 2016 Printed January 31, 2017
https://doi.org/10.4134/BKMS.b150623
Copyright © The Korean Mathematical Society.
Hai-Lan Jin, Fatma Kaynarca, Tai Keun Kwak, and Yang Lee
Yanbian University, Afyon Kocatepe University, Daejin University, Pusan National University
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
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