---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/Algebras/QuaternionAlgebras/bibliography.html"
source: "https://docs.magma-maths.org/Algebras/QuaternionAlgebras/bibliography.md"
part: "Algebras"
chapter: "Quaternion Algebras"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Algebras", "source": "../index-algebras.md"}
  - {"title": "Quaternion Algebras", "source": "index-quaternion-algebras.md"}
prev: {"title": "Units and Unit Groups", "source": "unit-group.md"}
next: {"title": "Algebras with Involution", "source": "../AlgebrasWithInvolution/index-algebras-with-involution.md"}
---

# Bibliography

<a id="cite-dembele-donnelly"></a>
- **[DD08]** L. Dembele and S. Donnelly. Computing Hilbert Modular Forms Over Fields With Nontrivial Class Group. In S. Pauli F. Hess and M.Pohst, editors, *ANTS VIII*, volume 5011 of LNCS. Springer-Verlag, 2008.
<a id="cite-denert88"></a>
- **[DG88]** M. Denert and J. Van Geel. The Class Number of Hereditary Orders in Non-Eichler Algebras over Global Fields. *Math. Ann.*, 282:379–393, 1988.
<a id="cite-fr1"></a>
- **[Fri97]** Carsten Friedrichs. Berechnung relativer Ganzheitsbasen mit dem Round-2-Algorithmus. Master's thesis, Technische Universität Berlin, 1997. http://www.math.tu-berlin.de/$\sim$kant/publications/diplom/friedrichs.ps.gz.
<a id="cite-forms-fqx"></a>
- **[Ger03]** Larry J. Gerstein. Definite quadratic forms over $\F_q[X]$. *J. Algebra*, 268(1):252–263, 2003.
<a id="cite-ivanyos-ronyai"></a>
- **[IR93]** Gábor Ivanyos and Lajos Rónyai. Finding maximal orders in semisimple algebras over ${\bf Q}$. *Comput. Complexity*, 3(3):245–261, 1993.
<a id="cite-kirschmer-voight"></a>
- **[KV10]** M. Kirschmer and J. Voight. Algorithmic enumeration of ideal classes for quaternion orders. *SIAM J. Comput. (SICOMP)*, 39(5):1714–1747, 2010.
<a id="cite-reiner-mo"></a>
- **[Rei03]** Irving Reiner. *Maximal Orders*. Volume 28 of LMS Monographs. Oxford University Press, 2003.
<a id="cite-vigneras76"></a>
- **[Vig76]** M.-F. Vignéras. Simplification pour les ordres des corps de quaternions totalement définits. *J. Reine Angew. Math.*, 286-287:257–277, 1976.
<a id="cite-vigneras80"></a>
- **[Vig80]** M.-F. Vignéras. *Arithmétique des Algèbres de Quaternions*. Volume 800 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1980.
<a id="cite-voight1"></a>
- **[Voi05]** John Voight. *Quadratic forms and quaternion algebras: Algorithms and arithmetic*. Dissertation, University of California, Berkeley, 2005.
<a id="cite-voight3"></a>
- **[Voi11]** J. Voight. “Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms.” 2011.