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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

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

Roberto, Kaique Matias de Andrade 20 February 2019 (has links)
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. / 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.

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