Brzezinski, Juliusz Definite quaternion orders of class number one. (English) Zbl 0843.11048 J. Théor. Nombres Bordx. 7, No. 1, 93-96 (1995). It is shown that there are exactly 25 isomorphism classes of definite quaternion orders of class number one over \(\mathbb{Z}\); they are listed explicitly. It is remarkable that 23 of the orders are Gorenstein orders and 2 are non-Gorenstein orders. Reviewer: M.Peters (Münster) Cited in 7 Documents MSC: 11R54 Other algebras and orders, and their zeta and \(L\)-functions Keywords:isomorphism classes of definite quaternion orders of class number one PDF BibTeX XML Cite \textit{J. Brzezinski}, J. Théor. Nombres Bordx. 7, No. 1, 93--96 (1995; Zbl 0843.11048) Full Text: DOI Numdam EuDML EMIS OpenURL References: [1] Brandt, H., Intrau, O., Tabellen reduzirter positiver ternärer quadratischer Formen, Abh. der Sächsischen Akad. der Wissenschaften zu Leipzig45 (1958). · Zbl 0082.03803 [2] Brzezinski, J., On orders in quaternion algebras, Comm. Alg.11 (1983), 501-522. · Zbl 0517.16006 [3] Brzezinski, J., On automorphisms of quaternion orders, J. Reine angew. Math.403 (1990), 166-186. · Zbl 0678.16003 [4] Curtis, C.W., Reiner, I., Methods of Representation Theory, vol. I, New-York1981. · Zbl 0616.20001 [5] Körner, O., Traces of Eichler-Brandt matrices and type numbers of quaternion orders, Proc. Indian Acad. Sci. (Math. Sci.)97 (1987), 189-199. · Zbl 0651.12011 [6] Vignéras, M.-F., Arithmétique des Algèbres de Quaternions, 800, Berlin-Heidelberg-New York1980. · Zbl 0422.12008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.