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Journal Articles International Journal of Number Theory Year : 2013

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

Abstract

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 and versions

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

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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. International Journal of Number Theory, 2013, 9 (3), pp.653-673. ⟨10.1142/S1793042112501540⟩. ⟨hal-00738164v2⟩
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