Localization and ideal theory in iterated differential operator rings

DOI10.1016/0021-8693(87)90003-2zbMath0608.16033OpenAlexW1988750694MaRDI QIDQ1086331

Allen D. Bell

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90003-2

zbMATH Keywords

global dimensionKrull dimensionsecond layer conditionartinian ringnoetherian P.I. ringiterated differential operator ringsclique localizationcliques of prime idealsfinite-dimensional Lie k-algebrasimple noetherian ringskew enveloping algebra

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Universal enveloping (super)algebras (17B35) Homological dimension in associative algebras (16E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (14)

Links between prime ideals in differential operator rings ⋮ Localization and ideal theory in Noetherian strongly group-graded rings ⋮ The second layer condition for certain centralizing extensions of FBN rings and polynomal rings ⋮ Localization and ideal theory in iterated differential operator rings ⋮ Prime Ideals in Differential Operator Rings. Catenarity ⋮ Extensions de ore d'anneaux noetheriens á i.p ⋮ Localization in rings equipped with an action of a solvable Lie algebra ⋮ Homological algebra in the category \(\text{Mod}_{(R\#U(g))}\) ⋮ Prime links in some skew-polynomial and skew-laurent rings ⋮ Classical localizability in solvable enveloping algebras and Poincaré- Birkhoff-Witt extensions ⋮ Localization and Catenarity in Iterated Differential Operator Rings ⋮ Prime ideals in skew polynomial rings and quantized Weyl algebras ⋮ Sur la cohomologie_-fine ⋮ Locally finite representations over Noetherian Hopf algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Differential operator rings whose prime factors have bounded Goldie dimension
• Links between prime ideals in differential operator rings
• Smash products and outer derivations
• Localization and ideal theory in iterated differential operator rings
• Prime ideals in differential operator rings and crossed products of infinite groups
• Module extensions over Noetherian rings
• Noetherian bimodules, primary decomposition, and Jacobson's conjecture
• Primitivity in differential operator rings
• Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
• A Goldie theorem for differentiably prime rings
• Einfache Derivationspolynomringe
• Ideaux premiers de l'algèbre enveloppante d'une algèbre de Lie nilpotente
• Krull and Global Dimensions of Fully Bounded Noetherian Rings
• Krull Versus Global Dimension in Noetherian P.I. Rings
• Ideals in universal enveloping algebras of solvable lie algebras
• Solvable lie algebras polycyclic-by-finite groups and bimodule krull dimension
• Noetherian Ore Extensions and Jacobson Rings
• Representations of Solvable Lie Algebras and the Gelfand-Kirillov Conjecture
• Localization in Non-Commutative Noetherian Rings
• Nil Rings Satisfying Certain Chain Conditions
• Corrigendum: Localisation in Enveloping Rings
• Global Dimension of Differential Operator Rings
• Krull Dimension of Differential Operator Rings

This page was built for publication: Localization and ideal theory in iterated differential operator rings