Números inteiros de Eisenstein - Lisboa, Diego de Lima (2017)
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.