Introduction To Commutative Algebra / Michael Francis Atiyah, & I G Macdonald.

Chapter 1 Rings and Ideals
Chapter 2 Modules
Chapter 3 Rings and Modules of Fractions
Chapter 4 Primary Decomposition
Chapter 5 Integral Dependence and Valuations
Chapter 6 Chain Conditions
Chapter 7 Noetherian Rings
Chapter 8 Artin Rings
Chapter 9 Discrete Valuation Rings and Dedekind Domains
Chapter 10 Completions .
Chapter 11 Dimension Theory
Index

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of providing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts on commutative algebra such as Zariski-Samuel [4] or Bourbaki [1]. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott [3] and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization