A quadratic field which is Euclidean but not norm-Euclidean
type: Item
instance of: scholarly article
title: A quadratic field which is Euclidean but not norm-Euclidean
zbMATH Open document ID: 0817.11047
DOI: 10.1007/BF02567617
author: David A. Clark
published in: Manuscripta Mathematica
publication date: 1995-08-08T00:00:00Z
full work available at URL: https://eudml.org/doc/155964
review text: The author uses earlier methods of \textit{E. S. Barnes} and \textit{H. P. F. Swinnerton-Dyer} [Acta Math. 87, 259-323 (1952; Zbl 0046.276)] to prove with the help of a computer that the ring \(\mathbb{Z}[ {{1+ \sqrt {69}} \over 2}]\) is Euclidean. This is the first example of a quadratic number field shown to be Euclidean but not norm-Euclidean.
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11Y40
Mathematics Subject Classification ID: 11A05
zbMATH DE Number: 624939
zbMATH Keywords: Euclidean quadratic field
Wikidata QID: Q55899107
reviewed by: Michael E. Pohst
MaRDI profile type: Publication
cites work: The inhomogeneous minima of binary quadratic forms. I
cites work: Q4320503
cites work: Q4154621
cites work: Quadratische Zahlkörper mit Euklidischem Algorithmus
cites work: Q4773795
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description: scientific article; zbMATH DE number 624939