Conjuntos algébricos: propriedades e resultados

Abstract

This work presents an elementary introduction to the domain of Algebraic Geometry, focusing on one of the main study objects in the area: algebraic sets. The paper aims to describe concepts and properties of algebraic sets from an algebraic, geometric and analytical point of view. Classical theorems, such as Hilbert's Basis Theorem and Hilbert's Nullstellensatz, the Zariski's Topology and the notions of algebraic variety, coordinate ring, local ring, multiplicity and dimension were explored throughout this work. For this construction, we have previously studied contents regarded as prerequisites, such as definitions and basic results of Linear Algebra, Abstract Algebra and Topology.