A quadratic field which is Euclidean but not norm-Euclidean

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1994 Germany English Publisher:Springer Science and Business Media LLCJournal:Manuscripta Mathematica, volume 83, pages 327-330 (issn: 0025-2611, eissn: 1432-1785,

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Authors: Clark, David A.;

doi: 10.1007/bf02567617

A quadratic field which is Euclidean but not norm-Euclidean

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Abstract

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.

Country

Germany

Related Organizations

Brigham Young University Idaho
United States
DigiZeitschriften
Germany

Keywords

Quadratic extensions, 510.mathematics, Euclidean quadratic field, Algebraic number theory computations, Multiplicative structure; Euclidean algorithm; greatest common divisors, Article

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