Commutative algebra with a view toward algebraic geometry

Table of Contents

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   Book Overview
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   Chapter 1 Introduction
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   Chapter 2 Elementary Definitions
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   Chapter 3 Roots of Commutative Algebra
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   Chapter 4 Localization
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   Chapter 5 Associated Primes and Primary Decomposition
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   Chapter 6 Integral Dependence and the Nullstellensatz
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   Chapter 7 Filtrations and the Artin-Rees Lemma
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   Chapter 8 Flat Families
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    Chapter 9 Completions and Hensel’s Lemma
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    Chapter 10 Introduction to Dimension Theory
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    Chapter 11 Fundamental Definitions of Dimension Theory
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    Chapter 12 The Principal Ideal Theorem and Systems of Parameters
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    Chapter 13 Dimension and Codimension One
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    Chapter 14 Dimension and Hilbert-Samuel Polynomials
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    Chapter 15 The Dimension of Affine Rings
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    Chapter 16 Elimination Theory, Generic Freeness, and the Dimension of Fibers
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    Chapter 17 Gröbner Bases
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    Chapter 18 Modules of Differentials
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    Chapter 19 Regular Sequences and the Koszul Complex
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    Chapter 20 Depth, Codimension, and Cohen-Macaulay Rings
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    Chapter 21 Homological Theory of Regular Local Rings
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    Chapter 22 Free Resolutions and Fitting Invariants
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    Chapter 23 Duality, Canonical Modules, and Gorenstein Rings