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

• Ano de defesa: 2019
• Autor(a) principal: Roberto, Kaique Matias de Andrade
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Functorial picture; Grupo especial; Multi-anéis; Multirings; Quadro funtorial; Real semigroup; Semigrupo real; Special group
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-25042019-095149/

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.