Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms

Detalhes bibliográficos
Autor(a) principal: Roberto, Kaique Matias de Andrade
Data de Publicação: 2019
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
Texto Completo: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-25042019-095149/
Resumo: The aim of this work is to establish precisely what are the functorial connections between the abstract theories of quadratic forms, as well as, to create a short and introductory path from the classic theory to the abstract ones. There is a large amount of literature developed about classic and abstract theories but does note relate them ``geographically\'\'. In this perspective, we discuss the fundamental aspects of the classic and reduced theory of quadratic forms, and sum up the theories of Quaternionic Structures, Cordes Schemes, Abstract Witt Rings, Abstract Ordering Spaces, Special Groups, Abstract Real Spectra and Real Semigroups in a functorial picture, inserting the new aspects involve the recent theory of Multirings and Multifields.
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spelling Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic formsMultianeis e a Câmara Secreta: relações funtoriais entre teorias abstratas de formas quadraticasFunctorial pictureGrupo especialMulti-anéisMultiringsQuadro funtorialReal semigroupSemigrupo realSpecial groupThe aim of this work is to establish precisely what are the functorial connections between the abstract theories of quadratic forms, as well as, to create a short and introductory path from the classic theory to the abstract ones. There is a large amount of literature developed about classic and abstract theories but does note relate them ``geographically\'\'. In this perspective, we discuss the fundamental aspects of the classic and reduced theory of quadratic forms, and sum up the theories of Quaternionic Structures, Cordes Schemes, Abstract Witt Rings, Abstract Ordering Spaces, Special Groups, Abstract Real Spectra and Real Semigroups in a functorial picture, inserting the new aspects involve the recent theory of Multirings and Multifields.O principal objetivo deste trabalho é estabelecer precisamente quais são as conexões funtoriais entre as teorias abstratas de formas quadráticas, criando uma via introdutória entre a teoria clássica e as abstratas durante este processo. Há uma gama de literatura desenvolvida tanto na teoria clássica quanto nas abstratas, mas nenhuma intercalando-as ``geograficamente\'\'. Nesta perspectiva, discutiremos os aspectos fundamentais da teoria clássica e reduzida de formas quadráticas, encapsulando as teorias das Estruturas Quaterniônicas, Esquemas de Cordes, Anéis de Witt Abstratos, Espaços de Ordens Abstratos, Grupos Especiais, Espectro Real Abstratos e Semigrupos Reais em um quadro funtorial, inserindo os novos elementos envolvendo a teoria recente dos Multi-anéis e Multi-corpos.Biblioteca Digitais de Teses e Dissertações da USPMariano, Hugo LuizRoberto, Kaique Matias de Andrade2019-02-20info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://www.teses.usp.br/teses/disponiveis/45/45131/tde-25042019-095149/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/openAccesseng2019-08-22T21:20:04Zoai:teses.usp.br:tde-25042019-095149Biblioteca 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:27212019-08-22T21:20:04Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false
dc.title.none.fl_str_mv Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
Multianeis e a Câmara Secreta: relações funtoriais entre teorias abstratas de formas quadraticas
title Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
spellingShingle Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
Roberto, Kaique Matias de Andrade
Functorial picture
Grupo especial
Multi-anéis
Multirings
Quadro funtorial
Real semigroup
Semigrupo real
Special group
title_short Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
title_full Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
title_fullStr Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
title_full_unstemmed Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
title_sort Multirings and The Chamber of Secrets: relationships between abstract theories of quadratic forms
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 Functorial picture
Grupo especial
Multi-anéis
Multirings
Quadro funtorial
Real semigroup
Semigrupo real
Special group
topic Functorial picture
Grupo especial
Multi-anéis
Multirings
Quadro funtorial
Real semigroup
Semigrupo real
Special group
description The aim of this work is to establish precisely what are the functorial connections between the abstract theories of quadratic forms, as well as, to create a short and introductory path from the classic theory to the abstract ones. There is a large amount of literature developed about classic and abstract theories but does note relate them ``geographically\'\'. In this perspective, we discuss the fundamental aspects of the classic and reduced theory of quadratic forms, and sum up the theories of Quaternionic Structures, Cordes Schemes, Abstract Witt Rings, Abstract Ordering Spaces, Special Groups, Abstract Real Spectra and Real Semigroups in a functorial picture, inserting the new aspects involve the recent theory of Multirings and Multifields.
publishDate 2019
dc.date.none.fl_str_mv 2019-02-20
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://www.teses.usp.br/teses/disponiveis/45/45131/tde-25042019-095149/
url http://www.teses.usp.br/teses/disponiveis/45/45131/tde-25042019-095149/
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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