Quaternion orders over quadratic integer rings from arithmetic fuchsian groups

Detalhes bibliográficos
Autor(a) principal: Carvalho, Edson Donizete de
Data de Publicação: 2012
Outros Autores: Andrade, Antonio Aparecido de [UNESP], Palazzo Júnior, Reginaldo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://www.diogenes.bg/ijam/contents/index.html
http://hdl.handle.net/11449/122734
Resumo: In this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.
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spelling Quaternion orders over quadratic integer rings from arithmetic fuchsian groupsHilbert symbolarithmetic Fuchsian groupquaternion ordercoding theoryIn this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.Universidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, BrasilUniversidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, BrasilUniversidade Estadual Paulista (Unesp)Carvalho, Edson Donizete deAndrade, Antonio Aparecido de [UNESP]Palazzo Júnior, Reginaldo2015-04-27T11:55:59Z2015-04-27T11:55:59Z2012info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article393-404http://www.diogenes.bg/ijam/contents/index.htmlInternational Journal of Applied Mathematics, v. 25, n. 3, p. 393-404, 2012.1311-1728http://hdl.handle.net/11449/12273489404983474819826300326709529109Currículo Lattesreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Applied Mathematicsinfo:eu-repo/semantics/openAccess2021-10-22T17:27:46Zoai:repositorio.unesp.br:11449/122734Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:45:37.514617Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
title Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
spellingShingle Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
Carvalho, Edson Donizete de
Hilbert symbol
arithmetic Fuchsian group
quaternion order
coding theory
title_short Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
title_full Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
title_fullStr Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
title_full_unstemmed Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
title_sort Quaternion orders over quadratic integer rings from arithmetic fuchsian groups
author Carvalho, Edson Donizete de
author_facet Carvalho, Edson Donizete de
Andrade, Antonio Aparecido de [UNESP]
Palazzo Júnior, Reginaldo
author_role author
author2 Andrade, Antonio Aparecido de [UNESP]
Palazzo Júnior, Reginaldo
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Carvalho, Edson Donizete de
Andrade, Antonio Aparecido de [UNESP]
Palazzo Júnior, Reginaldo
dc.subject.por.fl_str_mv Hilbert symbol
arithmetic Fuchsian group
quaternion order
coding theory
topic Hilbert symbol
arithmetic Fuchsian group
quaternion order
coding theory
description In this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.
publishDate 2012
dc.date.none.fl_str_mv 2012
2015-04-27T11:55:59Z
2015-04-27T11:55:59Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://www.diogenes.bg/ijam/contents/index.html
International Journal of Applied Mathematics, v. 25, n. 3, p. 393-404, 2012.
1311-1728
http://hdl.handle.net/11449/122734
8940498347481982
6300326709529109
url http://www.diogenes.bg/ijam/contents/index.html
http://hdl.handle.net/11449/122734
identifier_str_mv International Journal of Applied Mathematics, v. 25, n. 3, p. 393-404, 2012.
1311-1728
8940498347481982
6300326709529109
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv International Journal of Applied Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 393-404
dc.source.none.fl_str_mv Currículo Lattes
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128224447692800

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