On commutativity of skew polynomials at zero
Bull. Korean Math. Soc. 2017 Vol. 54, No. 1, 51-69
Published online August 25, 2016
Printed January 31, 2017
Hai-Lan Jin, Fatma Kaynarca, Tai Keun Kwak, and Yang Lee
Yanbian University, Afyon Kocatepe University, Daejin University, Pusan National University
Abstract : 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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