Algebraic integers of pure sextic extensions

Detalhes bibliográficos
Autor(a) principal: de Andrade, Antonio Aparecido [UNESP]
Data de Publicação: 2022
Outros Autores: Facini, Linara Stéfani [UNESP], Esteves, Livea Cichito [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://hdl.handle.net/11449/248567
Resumo: Let K = Q(θ), where (Formula Presented), be a pure sextic field with d ≠ 1 a square free integer. In this paper, we characterize completely whether {1, θ,…, θ5} is an integral basis of K or do not. When d ≢ ±1,±17,±10,−15,−11,−7,−3, 5, 13(mod 36) we prove that K has a power integral basis. Furthermore, for the other cases we present an integral basis
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spelling Algebraic integers of pure sextic extensionsAlgebraic number fieldalgebraic number integerpure sextic extensionLet K = Q(θ), where (Formula Presented), be a pure sextic field with d ≠ 1 a square free integer. In this paper, we characterize completely whether {1, θ,…, θ5} is an integral basis of K or do not. When d ≢ ±1,±17,±10,−15,−11,−7,−3, 5, 13(mod 36) we prove that K has a power integral basis. Furthermore, for the other cases we present an integral basisFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Department of Mathematics S˜ao Paulo State University (Unesp) Institute of Biosciences Humanites and Exact Sciences (Ibilce) Campus S˜ao José do Rio PretoDepartment of Mathematics S˜ao Paulo State University (Unesp) Institute of Biosciences Humanites and Exact Sciences (Ibilce) Campus S˜ao José do Rio PretoFAPESP: 2013/25977-7Universidade Estadual Paulista (UNESP)de Andrade, Antonio Aparecido [UNESP]Facini, Linara Stéfani [UNESP]Esteves, Livea Cichito [UNESP]2023-07-29T13:47:29Z2023-07-29T13:47:29Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article112-124Journal of Prime Research in Mathematics, v. 18, n. 2, p. 112-124, 2022.1818-54951817-3462http://hdl.handle.net/11449/2485672-s2.0-85150884030Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Prime Research in Mathematicsinfo:eu-repo/semantics/openAccess2023-07-29T13:47:29Zoai:repositorio.unesp.br:11449/248567Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T13:47:29Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Algebraic integers of pure sextic extensions
title Algebraic integers of pure sextic extensions
spellingShingle Algebraic integers of pure sextic extensions
de Andrade, Antonio Aparecido [UNESP]
Algebraic number field
algebraic number integer
pure sextic extension
title_short Algebraic integers of pure sextic extensions
title_full Algebraic integers of pure sextic extensions
title_fullStr Algebraic integers of pure sextic extensions
title_full_unstemmed Algebraic integers of pure sextic extensions
title_sort Algebraic integers of pure sextic extensions
author de Andrade, Antonio Aparecido [UNESP]
author_facet de Andrade, Antonio Aparecido [UNESP]
Facini, Linara Stéfani [UNESP]
Esteves, Livea Cichito [UNESP]
author_role author
author2 Facini, Linara Stéfani [UNESP]
Esteves, Livea Cichito [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv de Andrade, Antonio Aparecido [UNESP]
Facini, Linara Stéfani [UNESP]
Esteves, Livea Cichito [UNESP]
dc.subject.por.fl_str_mv Algebraic number field
algebraic number integer
pure sextic extension
topic Algebraic number field
algebraic number integer
pure sextic extension
description Let K = Q(θ), where (Formula Presented), be a pure sextic field with d ≠ 1 a square free integer. In this paper, we characterize completely whether {1, θ,…, θ5} is an integral basis of K or do not. When d ≢ ±1,±17,±10,−15,−11,−7,−3, 5, 13(mod 36) we prove that K has a power integral basis. Furthermore, for the other cases we present an integral basis
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01
2023-07-29T13:47:29Z
2023-07-29T13:47:29Z
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 Journal of Prime Research in Mathematics, v. 18, n. 2, p. 112-124, 2022.
1818-5495
1817-3462
http://hdl.handle.net/11449/248567
2-s2.0-85150884030
identifier_str_mv Journal of Prime Research in Mathematics, v. 18, n. 2, p. 112-124, 2022.
1818-5495
1817-3462
2-s2.0-85150884030
url http://hdl.handle.net/11449/248567
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Prime Research in Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 112-124
dc.source.none.fl_str_mv Scopus
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_ 1803650098461147136

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