On \(SG_ n\) of orders
type: Item
instance of: scholarly article
title: On \(SG_ n\) of orders
zbMATH Open document ID: 0701.16009
DOI: 10.1016/0021-8693(90)90073-W
author: Reinhard Laubenbacher
author: David L. Webb
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let R be a Dedekind domain with field of fractions K, and let M be an R- order in a separable K-algebra A. The authors prove that, under certain conditions on R and M, \(SG_ n(M)=\ker (G_ n(M)\to G_ n(A))=0\) for all \(n\geq 1\). This generalizes a result of \textit{C. Soulé} [Invent. Math. 55, 251-295 (1979; Zbl 0437.12008)]. In particular, this theorem applies to the integral group ring of a finite group, i.e., \(SG_ n(RG)=0\) if G is a finite group and R is the ring of integers in a number field. When M is regular, e.g., when M is maximal, then \(SK_ n(M)=0\) for all \(n\geq 1\).
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 4148335
zbMATH Keywords: Grothendieck groups
zbMATH Keywords: R-order
zbMATH Keywords: separable K-algebra
zbMATH Keywords: integral group ring
zbMATH Keywords: finite group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4148335