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

• Ano de defesa: 2023
• Autor(a) principal: Roberto, Kaique Matias de Andrade
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: 2-grupos profinitos; Anéis graduados; Arason-Pfister hauptsatz; Formas quadráticas; Graded rings; Grupo especial; Hipercorpos; Hyperfield; Multi anéis; Multirings; Profinite 2-group; Quadratic forms; Special groups
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-22092023-151330/

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).