The simple modules of the ore extensions with coefficients from a dedekind ring

DOI10.1080/00927879908826587zbMath0944.16001OpenAlexW2077295239MaRDI QIDQ4254196

Vladimir V. Bavula

Publication date: 26 June 2000

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

Full work available at URL: https://doi.org/10.1080/00927879908826587

zbMATH Keywords

derivationsautomorphismssimple modulesirreducible elementsEuclidean ringsOre extensionscommutative Dedekind domains

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Euclidean rings and generalizations (13F07)

Related Items (17)

On prime and primitive ideals of the centrally extended Heisenberg double of SL₂ ⋮ Simple modules over Kq[X,Y⋊Uq≥0(sl2) and Kq[X,Y]⋊Uq(sl2) at root of unity] ⋮ Isomorphism problems and groups of automorphisms for Ore extensions 𝐾[𝑥[𝑦;𝛿] (zero characteristic)] ⋮ Adjoint functors raised from Ore extensions ⋮ The prime spectrum and simple modules over the quantum spatial ageing algebra ⋮ Classifications of prime ideals and simple modules of the Weyl algebra \(A_1\) in prime characteristic ⋮ Critical and injective modules over skew polynomial rings ⋮ The prime spectrum of the algebra \(\mathbb{K}_q[X,Y \rtimes U_q(\mathfrak{sl}_2)\) and a classification of simple weight modules] ⋮ Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2 ⋮ THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V₂) ⋮ MAXIMAL COMMUTATIVE SUBRINGS AND SIMPLICITY OF ORE EXTENSIONS ⋮ Torsion simple modules over the quantum spatial ageing algebra ⋮ The prime ideals and simple weight modules of the algebra 𝑈(𝔟⋉𝔙₃) ⋮ Classification of simple modules of the Ore extension \(K[X[Y; f\frac{d}{dX}]\)] ⋮ On representations of the centrally extended Heisenberg double of SL2 ⋮ Unnamed Item ⋮ Unnamed Item

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
• The simple modules of certain generalized crossed products
• Classification of the irreducible representations of 𝔰𝔩(2,ℭ)

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