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Pré-Publication, Document De Travail Année : 2012

Euclidean totally definite quaternion fields over the rational field and over quadratic number fields

Résumé

In this article we study totally definite quaternion fields over the rational field and over quadratic number fields. We establish a complete list of all such fields which are Euclidean. Moreover, we prove that every field in this list is in fact norm-Euclidean. The proofs are both theoretical and algorithmic.
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Dates et versions

hal-00738164 , version 1 (03-10-2012)
hal-00738164 , version 2 (13-05-2013)

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  • HAL Id : hal-00738164 , version 1

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Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski. Euclidean totally definite quaternion fields over the rational field and over quadratic number fields. 2012. ⟨hal-00738164v1⟩
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