Totally indefinite Euclidean quaternion fields

• Autorzy: Jean-Paul Cerri , Jérôme Chaubert , Pierre Lezowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16H10: Orders in separable algebras
• 16H05: Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
• 11Y40: Algebraic number theory computations
• 13F07: Euclidean rings and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 165
• Numer: 2
• Strony: 181-200

Daty

wydano

2014

Twórcy

autor

Jean-Paul Cerri

• Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France
• CNRS, IMB, UMR 5251, F-33400 Talence, France
• INRIA LFANT, F-33400 Talence, France

autor

Jérôme Chaubert

• rue du Talent, 1042 Malapalud, Suisse

autor

Pierre Lezowski

• INRIA LFANT, F-33400 Talence, France
• CNRS, IMB, UMR 5251, F-33400 Talence, France
• Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France

Identyfikatory

DOI

10.4064/aa165-2-4