An additivity principle for Goldie rank

DOI10.1007/BF02760541zbMath0395.17010OpenAlexW2056374930MaRDI QIDQ1252933

Lance W. Small, Anthony Joseph

Publication date: 1978

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02760541

zbMATH Keywords

Enveloping AlgebraFinite Dimensional Lie AlgebraGelfand-Kirillov DimensionGoldie RankPrime Ring

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Related Items (30)

Associated series and regular elements of Noetherian rings ⋮ Prime ideals in finite extensions of Noetherian rings ⋮ Sur le principe d’Additivite du rang pour des bimodules, II ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, II ⋮ Unnamed Item ⋮ Kostant's problem, Goldie rank and the Gelfand-Kirillov conjecture ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Goldie rank in the enveloping algebra of a semisimple Lie algebra. III ⋮ On the ring extensions arising from completely solvable Lie superalgebras ⋮ Dimension de gelfand-kirillov et decomposition primaire bilatere dans certaines algebres filtrees ⋮ Unnamed Item ⋮ Prime ideals in intermediate integral centralizing extensions of PI-rings ⋮ Polynomial Algebras Have Polynomial Growth ⋮ Finite Correspondence of Spectra in Noetherian Ring Extensions ⋮ Actions of Linearly Reductive Groups on Pi-Algebras ⋮ Flat embeddings of noetherian algebras in artinian rings ⋮ Overrings of primitive factor rings of \(U(sl(2,\mathbb{C}))\) ⋮ Rings of invariants of finite groups when the bad primes exist ⋮ Gel'fand-Kirillov dimension can go up in extension modules ⋮ Diagrammes de Dynkin et algèbres enveloppantes d'algèbres de lie semi-simples ⋮ Gelfand-kirillov dimension and affine pi rings ⋮ Chain conditions in intermediate normalizing extensions ⋮ On the variety of a highest weight module ⋮ Prime ideals in fixed rings II ⋮ Sur le principe d' additivite du rang pour des bimodules ⋮ Sur la dimension de gelfand-kirillov ⋮ Group-Graded Rings, Smash Products, and Group Actions

Cites Work

• Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
• Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
• Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple
• Orders in Artinian rings

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