Prime ideals in differential operator rings and crossed products of infinite groups

DOI10.1016/0021-8693(87)90022-6zbMath0611.16023OpenAlexW2020088481MaRDI QIDQ1087622

William Chin

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)90022-6

zbMATH Keywords

crossed productsLie algebraprime idealsincomparabilityring extensionsupper central seriesMartindale ring of quotientstwisted smash productsfinitely generated nilpotent

Mathematics Subject Classification ID

Group rings (16S34) Automorphisms and endomorphisms (16W20) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Solvable, nilpotent (super)algebras (17B30) Localization and associative Noetherian rings (16P50) Centralizing and normalizing extensions (16S20) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (20)

Computing the symmetric ring of quotients ⋮ La formule des hausteurs de tauvel dans les anneaux d'operateurs differentiels ⋮ Localization and ideal theory in iterated differential operator rings ⋮ Centred bimodules over prime rings: Closed submodules and applications to ring extensions ⋮ Prime ideals in restricted differential operator rings ⋮ Radicals of crossed products of enveloping algebras ⋮ Prime ideals in crossed products of abelian groups^∗ ⋮ Cohomology ring of differential operator rings. ⋮ Actions of divided power Hopf algebras ⋮ Closed and prime ideals in free centred extensions ⋮ Localization and Catenarity in Iterated Differential Operator Rings ⋮ Hochschild (co)homology of differential operator rings ⋮ Prime ideals of ore extensions ⋮ Sur la cohomologie_-fine ⋮ Prime Ideals in Enveloping Rings ⋮ Delta methods in enveloping rings ⋮ Invariant polynomials of Ore extensions by $q$-skew derivations ⋮ Rings Graded by Polycyclic-by-Finite Groups ⋮ Localisation in rings equipped with a solvable Lie algebra action ⋮ The inversion height of the free field is infinite.

Cites Work

• Unnamed Item
• Computing the symmetric ring of quotients
• Differential identities of prime rings
• Prime ideals in crossed products of finite groups
• Primitivity in differential operator rings
• Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
• Primitive ideals in enveloping algebras
• Crossed products over prime rings
• Semiprime and prime crossed products
• Liberal Extensions
• Representations of Solvable Lie Algebras and the Gelfand-Kirillov Conjecture
• Krull dimension

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