ABSTRACT

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.

chapter 1|16 pages

Rings and Ideals

chapter 2|19 pages

Modules

chapter 3|14 pages

Rings and Modules of Fractions

chapter 4|9 pages

Primary Decomposition

chapter 5|15 pages

Integral Dependence and Valuations

chapter 6|6 pages

Chain Conditions

chapter 7|9 pages

Noetherian Rings

chapter 8|4 pages

Artin Rings

chapter 10|16 pages

Completions

chapter 11|11 pages

Dimension Theory