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Exceptional units and Euclidean number fields

Authors
  • Houriet, Julien1
  • 1 Ecole Polytechnique Fédérale de Lausanne, Chaire de structures algébriques et géométriques, Lausanne, CH-1015, Switzerland , Lausanne (Switzerland)
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Birkhäuser-Verlag
Publication Date
Apr 04, 2007
Volume
88
Issue
5
Pages
425–433
Identifiers
DOI: 10.1007/s00013-006-1019-0
Source
Springer Nature
Keywords
License
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Abstract

By a result of H.W. Lenstra, one can prove that a number field is Euclidean with the aid of exceptional units. We describe two methods computing exceptional sequences, i.e., sets of units such that the difference of any two of them is still a unit. The second method is based on a graph theory algorithm for the maximum clique problem. This yielded 42 new Euclidean number fields in degrees 8, 9, 10, 11 and 12.

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