The influence of ideal structure on representation theory

DOI10.1016/0021-8693(88)90219-0zbMath0652.16006OpenAlexW2083646111MaRDI QIDQ1106922

Kenneth A. Brown, Robert B. jun. Warfield

Publication date: 1988

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(88)90219-0

zbMATH Keywords

prime idealannihilatorsecond layer conditionFBN ringsNoetherian ringprime spectrumlayersenveloping algebras of finite-dimensional solvable Lie algebrasgroup rings of polycyclic-by-finite groupsinjective indecomposable modulelink graphsnon-split extension of a uniform submodule

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Group rings (16S34) Universal enveloping (super)algebras (17B35) Noetherian rings and modules (associative rings and algebras) (16P40) Representation theory of associative rings and algebras (16Gxx) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (15)

Simple modules and their essential extensions for skew polynomial rings ⋮ Prime ideals in finite extensions of Noetherian rings ⋮ The fundamental prime ideals of a noetherian prime PI ring ⋮ Stability of Gelfand–Kirillov dimension for rings with the strong second layer condition ⋮ Unnamed Item ⋮ Prime spectra of quantum semisimple groups ⋮ Affiliated series and extensions of modules ⋮ Annihilator Primes and Foundation Primes ⋮ On the ring extensions arising from completely solvable Lie superalgebras ⋮ Prime ideals in skew polynomial rings and quantized Weyl algebras ⋮ Noetherian Ring Extensions with Trace Conditions ⋮ Reflexive ideals and injective modules over Noetherian v-H orders ⋮ Finite Correspondence of Spectra in Noetherian Ring Extensions ⋮ Prime ideals of \(q\)-commutative power series rings. ⋮ Injective modules and representational repleteness

Cites Work

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• Quadratic Extensions of Skew Fields
• On the Ideals of a Noetherian Ring
• Non-Artinian Essential Extensions of Simple Modules
• On the Representation Theory of Solvable Lie Algebras
• The structure of modules over polycyclic groups
• INJECTIVE MODULES FOR GROUP RINGS OF POLYCYCLIC GROUPS I
• Krull dimension

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