The structure of modules over polycyclic groups

DOI10.1017/S0305004100058151zbMath0455.16003OpenAlexW2042460326MaRDI QIDQ3903132

Kenneth A. Brown

Publication date: 1981

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100058151

zbMATH Keywords

prime idealspolycyclic-by-finite groupinductorsorbital prime idealscritical composition seriesabsolutely Hilbert domainfinitely generated right RG-moduleisolated orbital subgroupssubsources

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Representation theory of associative rings and algebras (16Gxx) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (13)

Localization and ideal theory in Noetherian strongly group-graded rings ⋮ Unnamed Item ⋮ The influence of ideal structure on representation theory ⋮ Induced resolutions and Grothendieck groups of polycyclic-by-finite groups ⋮ On the structure of certain injective modules over group algebras of soluble groups of finite rank ⋮ Algebras of bounded finite dimensional representation type ⋮ On the catenarity of virtually nilpotent mod-\(p\) Iwasawa algebras ⋮ Prime links in some skew-polynomial and skew-laurent rings ⋮ On the Ideals of a Noetherian Ring ⋮ Localization in Ore extensions of commutative Noetherian rings ⋮ MONOLITHIC MODULES OVER NOETHERIAN RINGS ⋮ Injective modules and representational repleteness ⋮ Localisation at cliques in group rings

Cites Work

• Unnamed Item
• Finiteness of the injective hull
• Jacobson's conjecture and modules over fully bounded Noetherian rings
• Skew polynomial rings over orders in Artinian rings
• On the Residual Simplicity of Certain Modules
• Prime Ideals in Group Rings of Polycyclic Groups
• A Note on the Artin-Rees Property of certain Polycyclic Group Algebras
• Rings of Quotients of Group Rings
• Quotient Rings of Group Rings
• On the Ring of Quotients of a Group Ring
• Artinian quotient rings of group rings

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