Ranks of \(K_n\) and \(G_n\) of orders and group rings of finite groups over integers in number fields
type: Item
instance of: scholarly article
title: Ranks of \(K_n\) and \(G_n\) of orders and group rings of finite groups over integers in number fields
zbMATH Open document ID: 0936.11067
DOI: 10.1016/S0022-4049(98)00010-3
author: Aderemi O. Kuku
published in: Journal of Pure and Applied Algebra
publication date: 2000-05-24T00:00:00Z
review text: Let \(F\) be a number field with ring of integers \(R\), let \(\Lambda\) be an \(R\)-order which spans a semisimple \(F\)-algebra \(\Sigma\) and let \(\Gamma\) be a maximal \(R\)-order in \(\Sigma\) that contains \(\Lambda\). It is shown that, for all \(n\geq 2\), \[ \text{rank }K_n(\Lambda)= \text{rank }G_n(\Lambda)= \text{rank }K_n(\Gamma)= \text{rank }K_n(\Sigma). \] The proofs use the localization exact sequence in Quillen \(K\)-theory together with devissage arguments to establish that the modular terms are finite.
Mathematics Subject Classification ID: 11R70
Mathematics Subject Classification ID: 19D50
Mathematics Subject Classification ID: 19F27
Mathematics Subject Classification ID: 11R54
zbMATH DE Number: 1308358
zbMATH Keywords: Quillen \(K\)-group
zbMATH Keywords: rank
zbMATH Keywords: orders
zbMATH Keywords: group rings
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308358