Classification of simple modules of the Ore extension \(K[X][Y; f\frac{d}{dX}]\)

DOI10.1007/S11786-019-00414-7zbMath1462.16027OpenAlexW2983765003MaRDI QIDQ782681

Vladimir V. Bavula

Publication date: 28 July 2020

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-019-00414-7

zbMATH Keywords

global dimensionprime idealKrull dimensionsimple moduleskew polynomial ringnormal elementcompletely prime ideal

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Commutative rings of differential operators and their modules (13N10) Rings of differential operators (associative algebraic aspects) (16S32) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items (3)

Isomorphism problems and groups of automorphisms for Ore extensions 𝐾[𝑥[𝑦;𝛿] (zero characteristic)] ⋮ Identities for a parametric Weyl algebra over a ring ⋮ Identities for subspaces of a parametric Weyl algebra

Cites Work

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• The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
• Finite dimensionality of \(\text{Ext}^ n\)'s and \(\text{Tor}_ n\)'s of simple modules over one class of algebras
• Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules
• The simple modules of the ore extensions with coefficients from a dedekind ring
• Classification of Simple Weight Modules over the Schrödinger Algebra

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