Números inteiros de Eisenstein

• Ano de defesa: 2017
• Autor(a) principal: Lisboa, Diego de Lima
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Mestrado Profissional em Matemática; UFPB
• Palavras-chave em Português: Inteiros; Anel; Eisenstein; Irredutíveis; Integers; Ring; Irreducible; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/11232

Based on the development of the Theory of Integer Numbers, the present work will study of the properties, theorems, lemmas and corollaries of this theory to a more general domain, known as the Eisesntein Integer Ring, represented by Z[ω], based on the relationship between them and the ring of the Gaussian Integer,Z[i], seeking to understand in a most signi cant, simplistic and systematic way the arithmetic of this ring, constructing the notions of divisibility between two integers of Eisenstein, how to determine a common maximum divisor, how to identify the irreducible ones, and what criteria to use, why certain prime elements in Z are not irreducible in Z[ω]. We will also construct the irreducible decomposition of this ring as well as demonstrate the uniqueness of this factorization. Our interest is helping to improve a better understanding of various problems involving whole numbers and The theory of Eisenstein's Integers.