Smash products and outer derivations
type: Item
instance of: scholarly article
title: Smash products and outer derivations
zbMATH Open document ID: 0602.16007
DOI: 10.1007/BF02786565
author: Jeffrey Bergen
author: Susan Montgomery
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Soient \(H\) une algèbre de dimension finie, \(R\) une algèbre et un \(H\)-module (à gauche), \(R\#H\) le produit croisé, \(R^H\) les \(H\)-invariants de \(R\). Le théorème principal de cet article suppose que \(R\#H\) est semi-premier et que tout idéal \(\ne (0)\) de \(R\#H\) a une intersection \(\ne 0\) avec \(R\). Dans ce cas, les AA. prouvent que (1) \(R^H\) est Goldie si et seulement si \(R\) est Goldie, et (2) \(R\) est noethérien si \(R^H\) est noethérien. Si, de plus, \(R\#H\) est premier, et \(R^H\) vérifie une identité polynômiale, alors \(R\) vérifie une telle identité. Ces résultats généralisent des résultats obtenus par S. Montgomery (quand \(H\) est l'algèbre de groupe d'un groupe fini) et par Kharchenko, Bergman et Popov (quand \(H\) est l'algèbre enveloppante restreinte d'une algèbre de Lie restreinte de dimension finie).
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16P50
zbMATH DE Number: 3970963
zbMATH Keywords: outer derivations
zbMATH Keywords: prime ring
zbMATH Keywords: smash product
zbMATH Keywords: ring of constants
zbMATH Keywords: finite-dimensional Hopf algebra
zbMATH Keywords: ideal intersection property
zbMATH Keywords: invariant ring
zbMATH Keywords: polynomial identity
zbMATH Keywords: Goldie ring
reviewed by: Earl J. Taft
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3970963