Módulos sobre anéis : propriedades estruturais e o teorema de Nullstellensatz

Abstract

This work aims to explore the concept of modules over rings, generalizing the concept of vector spaces. A detailed analysis of Noetherian and Artinian modules is presented, discussing their main properties, associated theorems and relevant examples in abstract algebra/algebraic geometry. The study includes graded modules and their applications in algebraic varieties, with a special focus on the Nullstellensatz Theorem. The results obtained provide a solid basis for the advanced study of module theory, especially at the intersection between algebra and algebraic geometry. Furthermore, vector spaces and modules are briefly compared, with the aim of understanding their distinctions and simila-rities, providing a broad view of structures and their applications in various mathematical contexts.