Radicals of crossed products of enveloping algebras

DOI10.1007/BF02787259zbMath0637.17006OpenAlexW1972406930MaRDI QIDQ1098922

Susan Montgomery, Jeffrey Bergen, Donald S.Passman

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1007/bf02787259

zbMATH Keywords

crossed productsderivationsJacobson radicalnil idealsenveloping algebrasexterior algebras

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Exterior algebra, Grassmann algebras (15A75) Noetherian rings and modules (associative rings and algebras) (16P40) Rings with polynomial identity (16Rxx) Radicals and radical properties of associative rings (16Nxx)

Related Items (14)

How far can we go with Amitsur's theorem in differential polynomial rings? ⋮ Ore extensions of Jacobson rings. ⋮ Jacobson radicals of ring extensions. ⋮ ℒ-Prime Rings Need Not Be Primary ⋮ Primeness, semiprimeness and prime radical of ore extensions ⋮ Rings with simple Lie rings of Lie and Jordan derivations ⋮ Localization and Catenarity in Iterated Differential Operator Rings ⋮ Semiprime Lie Rings of (Anti-)Symmetric Derivations of Commutative Rings ⋮ On the Jacobson Radical of Skew Polynomial Extensions of Rings Satisfying a Polynomial Identity ⋮ A criterion for primeness of enveloping algebras of Lie superalgebras ⋮ SKEW POWER SERIES RINGS OF DERIVATION TYPE ⋮ Prime Lie Rings of Derivations of Commutative Rings ⋮ On radicals of monomial algebras ⋮ Gelfand-Kirillov dimension of algebras with locally nilpotent derivations.

Cites Work

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• Smash products and outer derivations
• Prime ideals in differential operator rings and crossed products of infinite groups
• Primitivity in differential operator rings
• On differential rings and skew pulynomials
• Radicals Of Polynomial Rings
• Primitive Ideals of Enveloping Algebras Over Commutative Rings
• On Radicals of Skew Polynomial Rings of Derivation Type
• Jacobson Radical of Filtered Algebras
• Noetherian Ore Extensions and Jacobson Rings
• Universal Enveloping Algebras with Subexponential but not Polynomially Bounded Growth
• A skew polynomial ring over a jacobson ring need not be a jacobson ring
• Nil Pi-Rings

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