Krull dimension of generalized Weyl algebras and iterated skew polynomial rings: Commutative coefficients

DOI10.1006/jabr.1998.7482zbMath0923.16022OpenAlexW2034451024MaRDI QIDQ1271894

Freddy M. J. van Oystaeyen, Vladimir V. Bavula

Publication date: 18 February 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://hdl.handle.net/10067/250990151162165141

zbMATH Keywords

universal enveloping algebrasprime idealsKrull dimensiongeneralized Weyl algebrasquantum deformationscommutative Noetherian ringsiterated skew polynomial rings

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Universal enveloping (super)algebras (17B35) Commutative Noetherian rings and modules (13E05) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Universal enveloping algebras of Lie algebras (16S30)

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Maximal graded orders over crystalline graded rings. ⋮ Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras ⋮ The group of automorphisms of the Jacobian algebra \(\mathbb A_n\). ⋮ Gelfand–Kirillov dimension of generalized Weyl algebras (In memory of Guenter Rudolf Krause (1941–2015)) ⋮ Simple holonomic modules over the second Weyl algebra \(A_2\) ⋮ Stable rank of down-up algebras ⋮ The global dimension of the generalized Weyl algebras 𝑆⁻¹𝐾[𝐻,𝐶[𝑋,𝑌;𝜎,𝑎]] ⋮ The Carlitz algebras. ⋮ Some Homological Properties of SkewPBWExtensions ⋮ Introducing crystalline graded algebras. ⋮ Generalized Weyl algebras are tensor Krull minimal ⋮ Down–up algebras over a polynomial base ring 𝕂[t₁,…,t_n] ⋮ MONOLITHIC MODULES OVER NOETHERIAN RINGS ⋮ Down-up algebras and ambiskew polynomial rings ⋮ Krull dimension of generalized Weyl algebras with noncommutative coefficients

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