Absolute stable rank and Witt cancellation for noncommutative rings
type: Item
instance of: scholarly article
title: Absolute stable rank and Witt cancellation for noncommutative rings
zbMATH Open document ID: 0639.16015
DOI: 10.1007/BF01388785
author: Wilberd van der Kallen
author: Bruce A. Magurn
author: L. N. Vaserstein
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143553
review text: Bass introduced the notion of ``stable range'' conditions on a ring R in order to characterize those integers n for which every matrix in GL\({}_ n\)(R) can be row reduced to a matrix with the same last row and column as the identity matrix. Similar questions concerning orthogonal groups over commutative rings led M. R. Stein to introduce ``absolute stable range'' conditions for commutative rings. The authors of this paper take up the question of absolute stable range and its connection with cancellation of quadratic forms over non-commutative rings. They provide a concise survey of previous results and their interconnections (including some examples of rings whose stable ranges and absolute stable ranges differ) and prove several new and interesting theorems.
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 11E16
zbMATH DE Number: 4042106
zbMATH Keywords: Witt cancellation
zbMATH Keywords: \(GL_ n\)
zbMATH Keywords: orthogonal groups
zbMATH Keywords: absolute stable range
zbMATH Keywords: cancellation of quadratic forms
reviewed by: Michael R. Stein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4042106