Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings

Detalhes bibliográficos
Autor(a) principal: Roberto, Kaique Matias de Andrade
Data de Publicação: 2023
Tipo de documento: Tese
Idioma: eng
Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-22092023-151330/
Resumo: The aim of this work is to initiate the investigation of the precise mathematical relationships so that possible configuring a ``new adjoint\'\' situation between special groups, graded rings, 2-groups and profinite 2-groups. We focused in the first part of this program, i,e, in the relations between graded rings and special groups. In our investigations, the theory of multirings/hyperrings played a central role, and we got an interesting result: we have obtained an wide extension (to all special hyperfields, or special groups) of the validity of the Arason-Pfister Hauptsatz (\\cite) - a positive answer to a question posed by J. Milnor in a classical paper of 1970 (\\cite)- and applied that to obtain interesting properties of graded rings associated to special hyperfields (\\cite, \\cite).
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spelling Multialgebraic structures and applications in abstract theories of quadratic forms and graded ringsEstruturas multi-algébricas e aplicações em teorias abstratas de formas quadráticas e anéis graduados2-grupos profinitosAnéis graduadosArason-Pfister hauptsatzArason-Pfister hauptsatzFormas quadráticasGraded ringsGrupo especialHipercorposHyperfieldMulti anéisMultiringsProfinite 2-groupQuadratic formsSpecial groupsThe aim of this work is to initiate the investigation of the precise mathematical relationships so that possible configuring a ``new adjoint\'\' situation between special groups, graded rings, 2-groups and profinite 2-groups. We focused in the first part of this program, i,e, in the relations between graded rings and special groups. In our investigations, the theory of multirings/hyperrings played a central role, and we got an interesting result: we have obtained an wide extension (to all special hyperfields, or special groups) of the validity of the Arason-Pfister Hauptsatz (\\cite) - a positive answer to a question posed by J. Milnor in a classical paper of 1970 (\\cite)- and applied that to obtain interesting properties of graded rings associated to special hyperfields (\\cite, \\cite).O objetivo deste trabalho é iniciar a investigação de possíveis relações matemáticas que configurem um \"novo quadro adjunto\" entre grupos especiais, anéis graduados, 2-grupos e 2-grupos profinitos. Nós focamos na primeira parte deste programa, i.e. nas relações entre anéis graduados e grupos especiais. Em nossas investigações, a teoria dos multi anéis/hipercorpos desempenhou um papel central, e obtivemos um resultado interessante: uma ampla extensão (para todos os grupos/hipercorpos especiais) da validade do Arason-Pfister Hauptsatz (\\cite) - uma resposta positiva para uma questão formulada por J. Milnor no clássico artigo de 1970 (\\cite) - e aplicamos este resultado na obtenção de propriedades associadas aos anéis graduados provenientes de hipercorpos especiais (\\cite, \\cite).Biblioteca Digitais de Teses e Dissertações da USPMariano, Hugo LuizRoberto, Kaique Matias de Andrade2023-08-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfhttps://www.teses.usp.br/teses/disponiveis/45/45131/tde-22092023-151330/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2023-09-28T20:47:04Zoai:teses.usp.br:tde-22092023-151330Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212023-09-28T20:47:04Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false
dc.title.none.fl_str_mv Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
Estruturas multi-algébricas e aplicações em teorias abstratas de formas quadráticas e anéis graduados
title Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
spellingShingle Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
Roberto, Kaique Matias de Andrade
2-grupos profinitos
Anéis graduados
Arason-Pfister hauptsatz
Arason-Pfister hauptsatz
Formas quadráticas
Graded rings
Grupo especial
Hipercorpos
Hyperfield
Multi anéis
Multirings
Profinite 2-group
Quadratic forms
Special groups
title_short Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
title_full Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
title_fullStr Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
title_full_unstemmed Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
title_sort Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
author Roberto, Kaique Matias de Andrade
author_facet Roberto, Kaique Matias de Andrade
author_role author
dc.contributor.none.fl_str_mv Mariano, Hugo Luiz
dc.contributor.author.fl_str_mv Roberto, Kaique Matias de Andrade
dc.subject.por.fl_str_mv 2-grupos profinitos
Anéis graduados
Arason-Pfister hauptsatz
Arason-Pfister hauptsatz
Formas quadráticas
Graded rings
Grupo especial
Hipercorpos
Hyperfield
Multi anéis
Multirings
Profinite 2-group
Quadratic forms
Special groups
topic 2-grupos profinitos
Anéis graduados
Arason-Pfister hauptsatz
Arason-Pfister hauptsatz
Formas quadráticas
Graded rings
Grupo especial
Hipercorpos
Hyperfield
Multi anéis
Multirings
Profinite 2-group
Quadratic forms
Special groups
description The aim of this work is to initiate the investigation of the precise mathematical relationships so that possible configuring a ``new adjoint\'\' situation between special groups, graded rings, 2-groups and profinite 2-groups. We focused in the first part of this program, i,e, in the relations between graded rings and special groups. In our investigations, the theory of multirings/hyperrings played a central role, and we got an interesting result: we have obtained an wide extension (to all special hyperfields, or special groups) of the validity of the Arason-Pfister Hauptsatz (\\cite) - a positive answer to a question posed by J. Milnor in a classical paper of 1970 (\\cite)- and applied that to obtain interesting properties of graded rings associated to special hyperfields (\\cite, \\cite).
publishDate 2023
dc.date.none.fl_str_mv 2023-08-09
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://www.teses.usp.br/teses/disponiveis/45/45131/tde-22092023-151330/
url https://www.teses.usp.br/teses/disponiveis/45/45131/tde-22092023-151330/
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv
dc.rights.driver.fl_str_mv Liberar o conteúdo para acesso público.
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Liberar o conteúdo para acesso público.
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.coverage.none.fl_str_mv
dc.publisher.none.fl_str_mv Biblioteca Digitais de Teses e Dissertações da USP
publisher.none.fl_str_mv Biblioteca Digitais de Teses e Dissertações da USP
dc.source.none.fl_str_mv
reponame:Biblioteca Digital de Teses e Dissertações da USP
instname:Universidade de São Paulo (USP)
instacron:USP
instname_str Universidade de São Paulo (USP)
instacron_str USP
institution USP
reponame_str Biblioteca Digital de Teses e Dissertações da USP
collection Biblioteca Digital de Teses e Dissertações da USP
repository.name.fl_str_mv Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)
repository.mail.fl_str_mv virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br
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