Introdução a anéis e módulos Noetherianos e Artinianos

Abstract

This paper investigates the fundamental concepts of rings and modules, emphasizing the chain conditions that characterize Noetherian and Artinian structures. Rings, defined by two binary operations, and modules, which generalize vector spaces by replacing fields with rings, are presented as essential elements of abstract algebra. Our objective is to explore various examples of Noetherian and Artinian rings and modules through bibliographic research, utilizing recognized references such as Introduction to Commutative Algebra by M. F. Atiyah and I. G. Macdonald and Steps in Commutative Algebra by R. Y. Sharp. The structure of the paper includes an introductory chapter on the basic concepts of groups, followed by chapters exploring rings and modules, and finally, an introductory study on Noetherian and Artinian rings and modules, with illustrative examples and analyses aimed at facilitating the understanding of the topic.