Operations on orbits of unimodular vectors
type: Item
instance of: scholarly article
title: Operations on orbits of unimodular vectors
zbMATH Open document ID: 0592.20053
DOI: 10.1016/0021-8693(86)90088-8
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let A be an associative commutative ring with 1. Then \(GL_ nA\) and \(E_ nA\) act on the unimodular rows \(Um_ nA\subset A^ n\). The orbit set \(Um_ nA/E_ nA\) is the set of unimodular rows modulo the addition operations over A. The author introduces an action of the multiplicative semigroup of the integers on the set \(Um_ nA/E_ nA\) provided \(n\geq 3\). He shows that taking the m-power of an entry in \((a_ 1,...,a_ n)\in Um_ nA\) is a well-defined operation \(\psi_ m\) on \(Um_ nA/E_ nA\), \(n\geq 3\).
Mathematics Subject Classification ID: 20G35
zbMATH DE Number: 3950844
zbMATH Keywords: elementary matrices
zbMATH Keywords: unimodular rows
zbMATH Keywords: action
author: L. N. Vaserstein
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90088-8
OpenAlex ID: W2032057304
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description: scientific article; zbMATH DE number 3950844