Elementary divisor domains and Bézout domains
type: Item
instance of: scholarly article
title: Elementary divisor domains and Bézout domains
zbMATH Open document ID: 1266.13014
published in: Journal of Algebra
publication date: 2013-05-27T00:00:00Z
review text: Every elementary divisor domain is a Bézout domain; whether the converse holds is still an open question which dates as far back as 1942, (see \textit{O. Helmer} [Bull. Am. Math. Soc. 49, 225--236 (1943; Zbl 0060.07606)]). The paper under review addresses two issues. Firstly, it provides several hitherto unknown implications between an elementary divisor domain and a Bézout domain. Secondly, by starting with a commutative ring \(R\) which is not necessarily Bézout, the author constructs new Bézout rings associated with \(R\). In the methods employed, symmetric matrices, matrices with trace zero and linear homogeneous polynomials play a crucial role.
reviewed by: David Ssevviiri
Mathematics Subject Classification ID: 13F10
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 6166678
zbMATH Keywords: elementary divisor ring
zbMATH Keywords: Hermite ring
zbMATH Keywords: Bézout ring
zbMATH Keywords: rings defined by matrix properties
zbMATH Keywords: symmetric matrix
zbMATH Keywords: trace zero matrix
author: Dino Lorenzini
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2012.08.020
OpenAlex ID: W2100510730
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DOI: 10.1016/J.JALGEBRA.2012.08.020
description: scientific article; zbMATH DE number 6166678