The Hermite ring conjecture in dimension one
type: Item
instance of: scholarly article
title: The Hermite ring conjecture in dimension one
zbMATH Open document ID: 1151.13009
author: Ihsen Yengui
published in: Journal of Algebra
publication date: 2008-10-06T00:00:00Z
review text: Here is the author's abstract: ``We prove constructively that for any ring \textbf{R} of Krull dimension \(\leq1\) and \(n\geq3\), the group E\(_n({\mathbf R}[X])\) acts transitively on Um\(_n({\mathbf R}[X])\). In particular, we obtain that for any ring \textbf{R} with Krull dimension \(\leq 1\), all finitely generated stably free modules over \textbf{R}\([X]\) are free. This settles the long-standing Hermite ring conjecture for rings of Krull dimension \(\leq1\).'' In view of these results, the author conjectures that polynomial extensions in any number of indeterminates of a ring of Krull dimension \(\leq1\) are Hermite rings. The rings in this paper are commutative.
reviewed by: Moshe Roitman
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 19A13
zbMATH DE Number: 5349062
zbMATH Keywords: Constructive Mathematics
zbMATH Keywords: Hermite ring conjecture
zbMATH Keywords: Hermite ring
zbMATH Keywords: Quillen-Suslin theorem
zbMATH Keywords: stably free modules
zbMATH Keywords: unimodular rows
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.02.007
OpenAlex ID: W2076861157
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Wikidata QID: Q122980941
DOI: 10.1016/J.JALGEBRA.2008.02.007
description: scientific article; zbMATH DE number 5349062