Approximating rings of integers in number fields
type: Item
instance of: scholarly article
title: Approximating rings of integers in number fields
zbMATH Open document ID: 0828.11075
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1995-12-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/47309
full work available at URL: jtnb6-2.html
review text: This is a nice survey on the problem of computing the maximal order \(o_F\) of an algebraic number field \(F\). Starting from a result of \textit{A. L. Chistov} [Sov. Math., Dokl. 39, No. 3, 597-600 (1989); English translation from Dokl. Akad. Nauk SSSR 306, No. 5, 1063-1067 (1989; Zbl 0698.12001)] the authors discuss polynomial time algorithms for constructing an order of \(F\) which is close to \(o_F\) in a precise sense. Unfortunately the presentation is not very well balanced. Whereas several sections contain basic material from textbooks, others cover new ground - - at least from an algorithmic point of view. Notions like ``factor refinement'' are adopted uncritically although these ideals are certainly not new. They already were published by \textit{H. Zassenhaus} in the seventies [Symp. Math. 15, Convegni 1973, 499-513 (1975; Zbl 0337.12014)]\ and are contained in textbooks since more than five years.
Mathematics Subject Classification ID: 11Y40
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11R54
zbMATH DE Number: 754092
zbMATH Keywords: computing the maximal order of an algebraic number field
zbMATH Keywords: survey
zbMATH Keywords: polynomial time algorithms
author: Johannes Buchmann
author: H. W. jun. Lenstra
reviewed by: Michael E. Pohst
MaRDI profile type: Publication
OpenAlex ID: W2021409800
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DOI: 10.5802/JTNB.113
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description: scientific article; zbMATH DE number 754092