Commutative Algebra: with a View Toward
β David Eisenbud (auth.)
π Library
π
1995
π Springer New York
π English
β¦ LIBER β¦
π
Commutative Algebra: with a View Toward Algebraic Geometry
β Scribed by David Eisenbud (auth.)
- Publisher
- Springer New York
- Year
- 1995
- Tongue
- English
- Leaves
- 784
- Series
- Graduate Texts in Mathematics 150
- Edition
- Reprint of 1st edition
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
β¦ Table of Contents
Front Matter....Pages i-xvi
Introduction....Pages 1-10
Elementary Definitions....Pages 11-17
Front Matter....Pages 19-19
Roots of Commutative Algebra....Pages 21-56
Localization....Pages 57-86
Associated Primes and Primary Decomposition....Pages 87-115
Integral Dependence and the Nullstellensatz....Pages 117-144
Filtrations and the Artin-Rees Lemma....Pages 145-153
Flat Families....Pages 155-178
Completions and Henselβs Lemma....Pages 179-209
Front Matter....Pages 211-211
Introduction to Dimension Theory....Pages 213-224
Fundamental Definitions of Dimension Theory....Pages 225-229
The Principal Ideal Theorem and Systems of Parameters....Pages 231-246
Dimension and Codimension One....Pages 247-269
Dimension and Hilbert-Samuel Polynomials....Pages 271-280
The Dimension of Affine Rings....Pages 281-301
Elimination Theory, Generic Freeness, and the Dimension of Fibers....Pages 303-315
GrΓΆbner Bases....Pages 317-381
Modules of Differentials....Pages 383-415
Front Matter....Pages 417-417
Regular Sequences and the Koszul Complex....Pages 419-446
Depth, Codimension, and Cohen-Macaulay Rings....Pages 447-468
Front Matter....Pages 417-417
Homological Theory of Regular Local Rings....Pages 469-488
Free Resolutions and Fitting Invariants....Pages 489-517
Duality, Canonical Modules, and Gorenstein Rings....Pages 519-554
Back Matter....Pages 555-788
β¦ Subjects
Algebraic Geometry
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β David Eisenbud
π Library
π
1995
π Springer
π English
Commutative algebra, with a view toward
β David Eisenbud
π Library
π
1995
π Springer
π English
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition,