The Euclidean algorithm in algebraic number fields
type: Item
instance of: scholarly article
title: The Euclidean algorithm in algebraic number fields
zbMATH Open document ID: 0843.11046
author: Franz Lemmermeyer
published in: Expositiones Mathematicae
publication date: 1996-08-13T00:00:00Z
review text: This survey deals with the Euclidean algorithm and Euclidean minima in algebraic fields. Most work defines the Euclidean algorithm with respect to the norm function, but here other functions are also considered, as well as the \(k\)-stage algorithm first introduced by \textit{G. Cooke} [J. Reine Angew. Math. 282, 133-156 (1976; Zbl 0328.13013) and ibid. 283/284, 71-85 (1977; Zbl 0343.13008)]. Particular attention is paid to pointing out where unsolved problems exist and these are also shown by the gaps in the extensive tables of results. The bibliography contains 219 references, but unfortunately does not include all the papers cited in the survey, nor is it in strict alphabetical order, nor do the dates of papers always agree with the dates given in the survey. This is a pity, because it detracts a little from what is otherwise a valuable piece of work.
reviewed by: H. J. Godwin
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11-02
Mathematics Subject Classification ID: 11H50
Mathematics Subject Classification ID: 11A05
zbMATH DE Number: 849120
zbMATH Keywords: algebraic number fields
zbMATH Keywords: class number
zbMATH Keywords: survey
zbMATH Keywords: Euclidean algorithm
zbMATH Keywords: Euclidean minima
zbMATH Keywords: \(k\)-stage algorithm
zbMATH Keywords: unsolved problems
zbMATH Keywords: tables
zbMATH Keywords: bibliography
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 849120