• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  Bookmark and Share
Doctoral Thesis
Full name
Kaique Matias de Andrade Roberto
Knowledge Area
Date of Defense
São Paulo, 2023
Mariano, Hugo Luiz (President)
Dickmann, Maximo Alejandro
Lorscheid, Oliver
Miraglia Neto, Francisco
Petrovich, Alejandro Gustavo
Title in English
Multialgebraic structures and applications in abstract theories of quadratic forms and graded rings
Keywords in English
Arason-Pfister hauptsatz
Graded rings
Profinite 2-group
Quadratic forms
Special groups
Abstract in English
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).
Title in Portuguese
Estruturas multi-algébricas e aplicações em teorias abstratas de formas quadráticas e anéis graduados
Keywords in Portuguese
2-grupos profinitos
Anéis graduados
Arason-Pfister hauptsatz
Formas quadráticas
Grupo especial
Multi anéis
Abstract in Portuguese
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).
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
tese_kaique_final.pdf (1.67 Mbytes)
Publishing Date
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2024. All rights reserved.