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Commutative Algebra
Roots of Commutative Algebra
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Author(s):
David Eisenbud
Publication date
(Print):
1995
Publisher:
Springer New York
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Related collections
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory
Author and book information
Book Chapter
Publication date (Print):
1995
Pages
: 21-56
DOI:
10.1007/978-1-4612-5350-1_3
SO-VID:
4b7bd695-2881-4870-ac98-0fb988bb7a5e
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Book chapters
pp. 1
Introduction
pp. 11
Elementary Definitions
pp. 21
Roots of Commutative Algebra
pp. 57
Localization
pp. 87
Associated Primes and Primary Decomposition
pp. 117
Integral Dependence and the Nullstellensatz
pp. 145
Filtrations and the Artin-Rees Lemma
pp. 155
Flat Families
pp. 179
Completions and Hensel’s Lemma
pp. 213
Introduction to Dimension Theory
pp. 225
Fundamental Definitions of Dimension Theory
pp. 231
The Principal Ideal Theorem and Systems of Parameters
pp. 247
Dimension and Codimension One
pp. 271
Dimension and Hilbert-Samuel Polynomials
pp. 281
The Dimension of Affine Rings
pp. 303
Elimination Theory, Generic Freeness, and the Dimension of Fibers
pp. 317
Gröbner Bases
pp. 383
Modules of Differentials
pp. 419
Regular Sequences and the Koszul Complex
pp. 447
Depth, Codimension, and Cohen-Macaulay Rings
pp. 469
Homological Theory of Regular Local Rings
pp. 489
Free Resolutions and Fitting Invariants
pp. 519
Duality, Canonical Modules, and Gorenstein Rings
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