Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2009; 46(6): 1041-1050

Printed November 1, 2009

https://doi.org/10.4134/BKMS.2009.46.6.1041

Copyright © The Korean Mathematical Society.

Skew Laurent polynomial extensions of Baer and p.p.-rings

Alireza R. Nasr-Isfahani and Ahmad Moussavi

Tarbiat Modares University and Tarbiat Modares University

Abstract

Let $R$ be a ring and $\alpha$ a monomorphism of $R$. We study the skew Laurent polynomial rings $R[x,x^{-1};\alpha]$ over an $\alpha$-skew Armendariz ring $R$. We show that, if $R$ is an $\alpha$-skew Armendariz ring, then $R$ is a Baer (resp. p.p.-)ring if and only if $R[x,x^{-1};\alpha]$ is a Baer (resp. p.p.-)ring. Consequently, if $R$ is an Armendariz ring, then $R$ is a Baer (resp. p.p.-)ring if and only if $R[x,x^{-1}]$ is a Baer (resp. p.p.-)ring.

Keywords: skew Laurent polynomial rings, Baer rings, p.p.-rings, $\alpha$-rigid rings, skew-Armendariz rings

MSC numbers: 16S34, 16S36