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Displaying similar documents to “Representation fields for cyclic orders”

Totally indefinite Euclidean quaternion fields

Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski (2014)

Acta Arithmetica

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We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.