Dimensions of division rings

DOI10.1007/BF02760668zbMath0517.16014MaRDI QIDQ1053087

J. Toby Stafford

Publication date: 1983

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

zbMATH Keywords

group algebraKrull dimensionaugmentation idealsenveloping algebrasHirsch numberfinite-dimensional Lie algebraglobal homological dimensionGel'fand-Kirillov conjecturequotient division ringtorsion-free polycyclic-by-finite group

Mathematics Subject Classification ID

Group rings (16S34) Universal enveloping (super)algebras (17B35) Homological dimension in associative algebras (16E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Division rings and semisimple Artin rings (16Kxx)

Related Items (6)

Transcendence degree of division algebras. ⋮ The soluble subgroups and the Tits alternative in linear groups over rings of fractions of polycyclic group rings. I ⋮ \textit{LD}-stability for Goldie rings ⋮ A note on the Krull dimension of certain algebras ⋮ Hopf algebras with rigid dualizing complexes. ⋮ On lower transcendence degree

Cites Work

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• A dimension theorem for division rings
• Ideaux primitifs des algèbres enveloppantes
• Krull dimensions of the enveloping algebra of sl(2,C)
• Primitive ideals in enveloping algebras
• Krull dimension of noetherian algebras and extensions of the base field
• Zero Divisors and Idempotents in Group Rings
• Homological dimension and transcendence degree
• On the Dimension of Modules and Algebras, VIII. Dimension of Tensor Products
• On the Dimension of Group Rings
• ON THE HOMOLOGICAL DIMENSION OF GROUP ALGEBRAS OF SOLVABLE GROUPS

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