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Published online by Cambridge University Press: 16 April 2018
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.