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PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS

Part of: Radicals and radical properties of rings Modules, bimodules and ideals Conditions on elements Rings and algebras with additional structure Rings and algebras arising under various constructions

Published online by Cambridge University Press:  16 April 2018

CHRISTOPHER D. FISH  and
DAVID A. JORDAN
CHRISTOPHER D. FISH
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom e-mail: christopher.fish@cantab.net, d.a.jordan@sheffield.ac.uk
DAVID A. JORDAN
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom e-mail: christopher.fish@cantab.net, d.a.jordan@sheffield.ac.uk
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Abstract

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We determine sufficient criteria for the prime spectrum of an ambiskew polynomial algebra R over an algebraically closed field 𝕂 to be akin to those of two of the principal examples of such an algebra, namely the universal enveloping algebra U(sl2) (in characteristic 0) and its quantization Uq(sl2) (when q is not a root of unity). More precisely, we determine sufficient criteria for the prime spectrum of R to consist of 0, the ideals (z − λ)R for some central element z of R and all λ ∈ 𝕂, and, for some positive integer d and each positive integer m, d height two prime ideals P for which R/P has Goldie rank m.

MSC classification

Primary: 16S36: Ordinary and skew polynomial rings and semigroup rings
Secondary: 16D25: Ideals 16D30: Infinite-dimensional simple rings (except as in ) 16N60: Prime and semiprime rings 16W20: Automorphisms and endomorphisms 16W25: Derivations, actions of Lie algebras 16U20: Ore rings, multiplicative sets, Ore localization
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 49 - 68
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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