Tópicos de álgebra linear explorados com o auxílio da teoria de Galois

Detalhes bibliográficos
Autor(a) principal: Piotsckowski, Mônica
Data de Publicação: 2016
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Manancial - Repositório Digital da UFSM
Texto Completo: http://repositorio.ufsm.br/handle/1/28184
Resumo: Let L=K be a nite Galois extension. In this work, we explore the K-vector space Alt(L) of alternating bilinear forms over L. In particular, we present a decomposition of Alt(L) in direct sum. Also, we study the structure of Alt(L) in the case of cyclic Galois extension L=K. Another aspect of linear algebra that is explored in this dissertation are the K-endomorphisms over L with rank 1, that is, the K-hyperplanes of L.
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spelling 2023-03-14T14:37:57Z2023-03-14T14:37:57Z2016-05-10http://repositorio.ufsm.br/handle/1/28184Let L=K be a nite Galois extension. In this work, we explore the K-vector space Alt(L) of alternating bilinear forms over L. In particular, we present a decomposition of Alt(L) in direct sum. Also, we study the structure of Alt(L) in the case of cyclic Galois extension L=K. Another aspect of linear algebra that is explored in this dissertation are the K-endomorphisms over L with rank 1, that is, the K-hyperplanes of L.Seja L=K uma extens~ao de Galois nita. Neste trabalho, exploramos o K-espa co vetorial Alt(L) das formas bilineares alternadas sobre L. Em particular, apresentamos uma decomposi c~ao em soma direta de Alt(L). Tamb em estudamos a estrutura de Alt(L) no caso em que a extens~ao de Galois L=K e c clica. Outro aspecto de algebra linear que e abordado nesta disserta c~ao, s~ao os K-endomor smos de posto 1 de L, ou seja, os K-hiperplanos de L.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em MatemáticaUFSMBrasilMatemáticaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessExtensões de GaloisGrupo de GaloisFormas bilineares alternadasPostoExtensões cíclicasEndomor smosHiperplanosTraço GaloisGalois extensionsGalois groupAlternating bilinear formsRank, cyclic extensionEndomorphismsHyperplaneGalois traceCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICATópicos de álgebra linear explorados com o auxílio da teoria de GaloisLinear algebra topics explored with the help of Galois theoryinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisBagio, Dirceuhttp://lattes.cnpq.br/6329859285657492Tamusiunas, Thaisa RauppMachado, Gustavo Gringshttp://lattes.cnpq.br/5530279445866705Piotsckowski, Mônica100100000008600600600600600ec733a91-f0ee-4c80-844e-45dea6ee3df7bef04a86-f09f-4f79-9b0f-775806ad35beb4296afb-e543-45bc-8ea9-ba42a711bbb7d3030d87-05aa-42fe-8497-df3db5bb4590reponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGMATEMÁTICA_2016_PIOTSCKOWSKI_MÔNICA.pdfDIS_PPGMATEMÁTICA_2016_PIOTSCKOWSKI_MÔNICA.pdfDissertação de mestradoapplication/pdf418952http://repositorio.ufsm.br/bitstream/1/28184/1/DIS_PPGMATEM%c3%81TICA_2016_PIOTSCKOWSKI_M%c3%94NICA.pdfef5731db4ac566a0d6c8b6b2d49a7f75MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.ufsm.br/bitstream/1/28184/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81956http://repositorio.ufsm.br/bitstream/1/28184/3/license.txt2f0571ecee68693bd5cd3f17c1e075dfMD531/281842023-03-14 11:37:57.365oai:repositorio.ufsm.br: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ório Institucionalhttp://repositorio.ufsm.br/PUBhttp://repositorio.ufsm.br/oai/requestopendoar:39132023-03-14T14:37:57Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM)false
dc.title.por.fl_str_mv Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
dc.title.alternative.eng.fl_str_mv Linear algebra topics explored with the help of Galois theory
title Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
spellingShingle Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
Piotsckowski, Mônica
Extensões de Galois
Grupo de Galois
Formas bilineares alternadas
Posto
Extensões cíclicas
Endomor smos
Hiperplanos
Traço Galois
Galois extensions
Galois group
Alternating bilinear forms
Rank, cyclic extension
Endomorphisms
Hyperplane
Galois trace
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
title_full Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
title_fullStr Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
title_full_unstemmed Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
title_sort Tópicos de álgebra linear explorados com o auxílio da teoria de Galois
author Piotsckowski, Mônica
author_facet Piotsckowski, Mônica
author_role author
dc.contributor.advisor1.fl_str_mv Bagio, Dirceu
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/6329859285657492
dc.contributor.referee1.fl_str_mv Tamusiunas, Thaisa Raupp
dc.contributor.referee2.fl_str_mv Machado, Gustavo Grings
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/5530279445866705
dc.contributor.author.fl_str_mv Piotsckowski, Mônica
contributor_str_mv Bagio, Dirceu
Tamusiunas, Thaisa Raupp
Machado, Gustavo Grings
dc.subject.por.fl_str_mv Extensões de Galois
Grupo de Galois
Formas bilineares alternadas
Posto
Extensões cíclicas
Endomor smos
Hiperplanos
Traço Galois
topic Extensões de Galois
Grupo de Galois
Formas bilineares alternadas
Posto
Extensões cíclicas
Endomor smos
Hiperplanos
Traço Galois
Galois extensions
Galois group
Alternating bilinear forms
Rank, cyclic extension
Endomorphisms
Hyperplane
Galois trace
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Galois extensions
Galois group
Alternating bilinear forms
Rank, cyclic extension
Endomorphisms
Hyperplane
Galois trace
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
description Let L=K be a nite Galois extension. In this work, we explore the K-vector space Alt(L) of alternating bilinear forms over L. In particular, we present a decomposition of Alt(L) in direct sum. Also, we study the structure of Alt(L) in the case of cyclic Galois extension L=K. Another aspect of linear algebra that is explored in this dissertation are the K-endomorphisms over L with rank 1, that is, the K-hyperplanes of L.
publishDate 2016
dc.date.issued.fl_str_mv 2016-05-10
dc.date.accessioned.fl_str_mv 2023-03-14T14:37:57Z
dc.date.available.fl_str_mv 2023-03-14T14:37:57Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.uri.fl_str_mv http://repositorio.ufsm.br/handle/1/28184
url http://repositorio.ufsm.br/handle/1/28184
dc.language.iso.fl_str_mv por
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dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv UFSM
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Matemática
publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
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