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Abstract:

Let K be a totally real number field and let B be a totally definite quaternion algebra over K. Given a set of representatives for ideal classes for a maximal order in B, we show how to construct in an efficient way a set of representatives of ideal classes for any Bass order in B. The algorithm does not require any knowledge of class numbers, and improves the equivalence checking process by using a simple calculation with global units. As an application, we compute ideal classes representatives for an order of discriminant 30 in an algebra over the real quadratic field Q ([√ 5]. © 2014 American Mathematical Society.

Registro:

Documento: Artículo
Título:Computing ideal classes representatives in quaternion algebras
Autor:Pacetti, A.; Sirolli, N.
Filiación:Departamento de Matemática, Universidad de Buenos Aires - Pabellón I, Ciudad Universitaria (C1428EGA), Buenos Aires, Argentina
Año:2014
Volumen:83
Número:289
Página de inicio:2479
Página de fin:2507
DOI: http://dx.doi.org/10.1090/S0025-5718-2014-02796-8
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v83_n289_p2479_Pacetti

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Citas:

---------- APA ----------
Pacetti, A. & Sirolli, N. (2014) . Computing ideal classes representatives in quaternion algebras. Mathematics of Computation, 83(289), 2479-2507.
http://dx.doi.org/10.1090/S0025-5718-2014-02796-8
---------- CHICAGO ----------
Pacetti, A., Sirolli, N. "Computing ideal classes representatives in quaternion algebras" . Mathematics of Computation 83, no. 289 (2014) : 2479-2507.
http://dx.doi.org/10.1090/S0025-5718-2014-02796-8
---------- MLA ----------
Pacetti, A., Sirolli, N. "Computing ideal classes representatives in quaternion algebras" . Mathematics of Computation, vol. 83, no. 289, 2014, pp. 2479-2507.
http://dx.doi.org/10.1090/S0025-5718-2014-02796-8
---------- VANCOUVER ----------
Pacetti, A., Sirolli, N. Computing ideal classes representatives in quaternion algebras. Math. Comput. 2014;83(289):2479-2507.
http://dx.doi.org/10.1090/S0025-5718-2014-02796-8