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Exceptional units and Euclidean number fields

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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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  1. Chaire de structures algébriques et géométriques, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Julien Houriet

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  1. Julien Houriet
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Correspondence to Julien Houriet.

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Received: 16 May 2006

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Houriet, J. Exceptional units and Euclidean number fields. Arch. Math. 88, 425–433 (2007). https://doi.org/10.1007/s00013-006-1019-0

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  • DOI: https://doi.org/10.1007/s00013-006-1019-0

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