Quasi-Armendariz property for skew polynomial rings
Commun. Korean Math. Soc. 2011 Vol. 26, No. 4, 557-573
Printed December 1, 2011
Muhittin Ba\c{s}er and Tai Keun Kwak
Kocatepe University, Daejin University
Abstract : The concept of the quasi-Armendariz property of rings properly contains Armendariz rings and semiprime rings. In this paper, we extend the quasi-Armendariz property for a polynomial ring to the skew polynomial ring, hence we call such ring a $\sigma$-quasi-Armendariz ring for a ring endomorphism $\sigma$, and investigate its structures, several extensions and related properties. In particular, we study the semiprimeness and the quasi-Armendariz property between a ring $R$ and the skew polynomial ring $R[x;\sigma]$ of $R$, and so these provide us with an opportunity to study quasi-Armendariz rings and semiprime rings in a general setting, and several known results follow as consequences of our results.
Keywords : quasi-Armendariz property, skew polynomial ring, semiprime ring, rigid ring
MSC numbers : 16S36, 16N60, 16W20
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