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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| 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 |
| 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. |
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