G.肯珀著的《交换代数教程（英文版）》是一部交换代数的教程，讲述清晰透彻，方法新颖，比较侧重交换代数的几何意义，但是比Eisenbud的大字典要好读一些，同时也有相当的深度。可以作为一到两学期的教程或者自学的不错选择。本书以整个几何背景一脉相承，围绕着本领域优选了一些很重要的概念和结果。能够使读者更深入地学习书中的知识。尽管强调理论，但还是有三章集中讨论计算方面。图例和练习使得书中的知识更加丰富。
Introduction
Part I The Algebra-Geometry Lexicon
1 Hilbert's Nullstellensatz
1.1 Maximal Ideals
1.2 Jacobson Rings
1.3 Coordinate Rings
Exercises
2 Noetherian and Artinian Rings
2.1 The Noether and Artin Properties for Rings and Modules
2.2 Noetherian Rings and Modules
Exercises
3 The Zariski Topology
3.1 Affine Varieties
3.2 Spectra
3.3 Noetherian and Irreducible Spaces
Exercises
4 A Summary of the Lexicon
4.1 True Geometry: Affine Varieties
4.2 Abstract Geometry: Spectra
Exercises
Part II Dimension
5 Krull Dimension and Transcendence Degree
Exercises
6 Localization
Exercises
7 The Principal Ideal Theorem
7.1 Nal~yama's Lemma and the Principal Ideal Theorem
7.2 The Dimension of Fibers
Exercises
8 Integral Extensions
8.1 Integral Closure
8.2 Lying Over, Going Up, and Going Down
8.3 Noether Normalization
Exercises
Part III Computational Methods
9 Grobner Bases
9.1 Buchberger's Algorithm
9.2 First Application: Elimination Ideals
Exercises
10 Fibers and Images of Morphisms Revisited
10.1 The Generic Freeness Lemma
10.2 Fiber Dimension and Constructible Sets
10.3 Application: Invariant Theory
Exercises
11 Hilbert Series and Dimension
11.1 The Hilbert-Serre Theorem
11.2 Hilbert Polynomials and Dimension
Exercises
Part IV Local Rings
12 Dimension Theory
12.1 The Length of a Module
12.2 The Associated Graded Ring
Exercises
13 Regular Local Rings
13.1 Basic Properties of Regular Local Rings
13.2 The Jacobian Criterion
Exercises
14 Rings of Dimension One
14.1 Regular Rings and Normal Rings
14.2 Multiplicative Ideal Theory
14.3 Dedekind Domains
Exercises
Solutions of Some Exercises
References
Notation
Index
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