Mathematica Bohemica, Vol. 141, No. 3, pp. 385-405, 2016
Some properties of orders of quaternion algebras with regard to the discrete norm
Jan Horníček, Miroslav Kureš, Lenka Macálková
Received August 31, 2015. First published July 11, 2016.
Abstract: Quaternion algebras $(\frac{-1,b}{\mathbb{Q}})$ are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
Keywords: order in an imaginary quadratic field; order in a quaternion algebra; discretely normed ring; isomorphism; primitive algebra
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Affiliations: Jan Horníček, Miroslav Kureš, Institute of Mathematics, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic, e-mail: hhornicek@seznam.cz, kures@fme.vutbr.cz; Lenka Macálková, Global Change Research Centre Czech Academy of Sciences, v. v. i., Bělidla 4a, 603 00 Brno, Czech Republic, and Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic, e-mail: macalkoval@gmail.com
