K -Theory and Stable Structure of Some Noetherian Group Rings

DOI10.1112/plms/s3-42.2.193zbMath0427.16010OpenAlexW2075220893MaRDI QIDQ3864015

Kenneth A. Brown, J. Toby Stafford, Thomas H. Lenagan

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1112/plms/s3-42.2.193

zbMATH Keywords

maximal idealrelation modulesstable range theoremstability theoremsHirsch numberSerre's theoremsemimaximal idealpolycyclic-by- finite groupinfinite group ringsCancellation theorem

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Grothendieck groups, (K)-theory, etc. (16E20) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (9)

Generating modules efficiently: Algebraic K-theory for noncommutative Noetherian rings ⋮ Relation modules of polycyclic-by-finite groups ⋮ Module extensions over Noetherian rings ⋮ The IA-congruence kernel of high rank free metabelian groups ⋮ Ideal invariance and localization ⋮ Modules over polycyclic groups have many irreducible images ⋮ Invariants for distinguishing between stably isomorphic modules ⋮ Integral group rings: Groups of units and classical K-theory ⋮ Localisation at cliques in group rings

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