Números p-ádicos

We introduce and de ne the p-adics integer numbers as a result of a search for solutions, for a congruences system that derives from a variable polynomial equation with rational coe cients. We evidence that the p-adic integers set is strictly larger than the integers. We present a criterion so that...

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Detalles Bibliográficos
Autor: Gusmão, Ítalo Moraes de Melo
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2015
País:Brasil
Institución:Universidade Federal da Paraíba (UFPB)
Repositorio:Biblioteca Digital de Teses e Dissertações da UFPB
Idioma:portugués
OAI Identifier:oai:repositorio.ufpb.br:tede/9337
Acceso en línea:https://repositorio.ufpb.br/jspui/handle/tede/9337
Access Level:acceso abierto
Palabra clave:Teoria dos números
Corpo não-arquimediano
Números p- ádicos
Numbers theory
Non-Archimedean field
P-adic numbers
MATEMATICA::MATEMATICA APLICADA
Descripción
Sumario:We introduce and de ne the p-adics integer numbers as a result of a search for solutions, for a congruences system that derives from a variable polynomial equation with rational coe cients. We evidence that the p-adic integers set is strictly larger than the integers. We present a criterion so that a rational that holds a correspondent in a p-adic integers set. We search for the possibility to represent irrational and complex numbers as p-adics integers. Algebraically, the p-adic integers set will be an integral domain and, from this, we search for the construction of p-adic integers quotient eld so that shall form the p-adic rationals eld, from a purely algebraically point of view. In the second part, we will expose the bases for the construction of a norm that's di erent from the usual, establishing so a new metric in the rational numbers set and the construction of a non-archimedian eld.