Prime Ideals in Differential Operator Rings. Catenarity

DOI10.2307/2001486zbMath0692.16002OpenAlexW4243106311MaRDI QIDQ3033918

Kenneth A. Brown, Thomas H. Lenagan, Kenneth R. Goodearl

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2001486

zbMATH Keywords

derivationsaffine algebralattice of idealscatenaritylattice isomorphismformal differential operatorssaturated chains of prime idealscomparable primesfinite polynomial extensionsk- linear endomorphismsnoetherian k-algebra

Mathematics Subject Classification ID

Automorphisms and endomorphisms (16W20) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Noetherian rings and modules (associative rings and algebras) (16P40) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (6)

La formule des hausteurs de tauvel dans les anneaux d'operateurs differentiels ⋮ Prime ideals in skew Laurent polynomial rings ⋮ The global dimension of the algebras of polynomial integro-differential operators 𝕀n and the Jacobian algebras 𝔸n ⋮ Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules ⋮ Catenarity in rings with abelian group action ⋮ Catenarity and Gelfand-Kirillov dimension in Ore extensions

Cites Work

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• Differential operator rings whose prime factors have bounded Goldie dimension
• Localization and ideal theory in iterated differential operator rings
• Primitivity in differential operator rings
• Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
• A Goldie theorem for differentiably prime rings
• Non-commutative affine P. I. rings are catenary
• Catenarity and Gelfand-Kirillov dimension in Ore extensions
• Chains of Prime Ideals in Enveloping Algebras of Solvable Lie Algebras
• Noetherian Ore Extensions and Jacobson Rings
• Generic flatness and the nullstellensatz for ore extensions
• Localization and the AR Property

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