Algebraic integers of pure sextic extensions
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
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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Repositório Institucional da UNESP |
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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:29462024-08-05T21:27:12.789807Repositório 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_ |
1808129321329491968 |