EUCLIDEAN TOTALLY DEFINITE QUATERNION FIELDS OVER THE RATIONAL FIELD AND OVER QUADRATIC NUMBER FIELDS

DOI10.1142/S1793042112501540zbMath1280.11073MaRDI QIDQ4918853

Pierre Lezowski, Jérôme Chaubert, Jean-Paul Cerri

Publication date: 6 May 2013

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

quaternion algebramaximal ordernorm-Euclideanleft Euclidean

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Euclidean rings and generalizations (13F07) Totally real fields (11R80)

Related Items (6)

A dichotomy for integral group rings via higher modular groups as amalgamated products ⋮ Totally indefinite Euclidean quaternion fields ⋮ Abelianization and fixed point properties of units in integral group rings ⋮ Generating hyperbolic isometry groups by elementary matrices ⋮ The twisted Euclidean algorithm: applications to number theory and geometry ⋮ Computation of Euclidean minima in totally definite quaternion fields

Cites Work

• About Euclidean rings
• Corrigendum: Algorithmic Enumeration of Ideal Classes for Quaternion Orders
• Euclidean minima of totally real number fields: Algorithmic determination
• EUCLIDEAN MINIMA AND CENTRAL DIVISION ALGEBRAS
• The Euclidean algorithm

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