This book is designed to be read by students who have had a first elementary course in general algebra. It provides a common generalization of the primes of arithmetic and the points of geometry. The book explains the various elementary operations which can be performed on ideals.
Table of Contents
Introduction -- Notation and Terminology -- Rings and Ideals -- Modules -- Rings and Modules of Fractions -- Primary Decomposition -- Integral Dependence and Valuations -- Chain Conditions -- Noetherian Rings -- Artin Rings -- Discrete Valuation Rings and Dedekind Domains -- Completions -- Dimension Theory