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SKEW LAURENT POLYNOMIAL EXTENSIONS OF BAER AND P.P.-RINGS

  • Nasr-Isfahani, Alireza R. (Department of Mathematics Tarbiat Modares University) ;
  • Moussavi, Ahmad (Department of Mathematics Tarbiat Modares University)
  • Published : 2009.11.30

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.

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  1. Baer and Quasi-Baer Properties of Skew Generalized Power Series Rings vol.44, pp.4, 2016, https://doi.org/10.1080/00927872.2015.1027370
  2. On diameter of the zero-divisor and the compressed zero-divisor graphs of skew Laurent polynomial rings pp.1793-6829, 2018, https://doi.org/10.1142/S0219498819501263