Computing ideal classes representatives in quaternion algebras

Autores
Pacetti, Ariel Martín; Sirolli, Nicolás Martín
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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].
Fil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sirolli, Nicolás Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
IDEAL
CLASSES
QUATERNION
ALGEBRAS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/85175
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/85175
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Computing ideal classes representatives in quaternion algebrasPacetti, Ariel MartínSirolli, Nicolás MartínIDEALCLASSESQUATERNIONALGEBRAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let 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].Fil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Sirolli, Nicolás Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2014-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/85175Pacetti, Ariel Martín; Sirolli, Nicolás Martín; Computing ideal classes representatives in quaternion algebras; American Mathematical Society; Mathematics of Computation; 83; 289; 6-2014; 2479-25070025-5718CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2014-02796-8info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02796-8/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1007.2821info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:44:00Zoai:ri.conicet.gov.ar:11336/85175instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:44:01.263CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Computing ideal classes representatives in quaternion algebras
title Computing ideal classes representatives in quaternion algebras
spellingShingle Computing ideal classes representatives in quaternion algebras
Pacetti, Ariel Martín
IDEAL
CLASSES
QUATERNION
ALGEBRAS
title_short Computing ideal classes representatives in quaternion algebras
title_full Computing ideal classes representatives in quaternion algebras
title_fullStr Computing ideal classes representatives in quaternion algebras
title_full_unstemmed Computing ideal classes representatives in quaternion algebras
title_sort Computing ideal classes representatives in quaternion algebras
dc.creator.none.fl_str_mv Pacetti, Ariel Martín
Sirolli, Nicolás Martín
author Pacetti, Ariel Martín
author_facet Pacetti, Ariel Martín
Sirolli, Nicolás Martín
author_role author
author2 Sirolli, Nicolás Martín
author2_role author
dc.subject.none.fl_str_mv IDEAL
CLASSES
QUATERNION
ALGEBRAS
topic IDEAL
CLASSES
QUATERNION
ALGEBRAS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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].
Fil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sirolli, Nicolás Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description 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].
publishDate 2014
dc.date.none.fl_str_mv 2014-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/85175
Pacetti, Ariel Martín; Sirolli, Nicolás Martín; Computing ideal classes representatives in quaternion algebras; American Mathematical Society; Mathematics of Computation; 83; 289; 6-2014; 2479-2507
0025-5718
CONICET Digital
CONICET
url http://hdl.handle.net/11336/85175
identifier_str_mv Pacetti, Ariel Martín; Sirolli, Nicolás Martín; Computing ideal classes representatives in quaternion algebras; American Mathematical Society; Mathematics of Computation; 83; 289; 6-2014; 2479-2507
0025-5718
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2014-02796-8
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02796-8/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1007.2821
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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