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Commutative Algebra with a View Toward Algebraic Geometry

ISBN-10: 0387942696
ISBN-13: 9780387942698
Edition: 1995
Authors: David Eisenbud
List price: $49.95 Buy it from $24.21
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Description: 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  More...

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Book details

List price: $49.95
Copyright year: 1995
Publisher: Springer
Publication date: 3/1/1999
Binding: Paperback
Pages: 788
Size: 6.50" wide x 9.75" long x 1.75" tall
Weight: 3.344
Language: 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, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text.One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included.This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.

Introduction
Elementary Definitions
Roots of Commutative Algebra
Localization
Associated Primes and Primary Decomposition
Integral Dependence and the Nullstellensatz
Filtrations and the Artin-Rees Lemma
Flat Families
Completions and Hensel's Lemma
Introduction to Dimension Theory
Fundamental Definitions of Dimension Theory
The Principal Ideal Theorem and Systems of Parameters
Dimension and Codimension One
Dimension and Hilbert-Samuel Polynomials
The Dimension of Affine Rings
Elimination Theory, Generic Freeness, and the Dimension of Fibers
Grobner Bases
Modules of Differentials
Regular Sequences and the Koszul Complex
Depth, Codimension, and Cohen-Macaulay Rings
Homological Theory of Regular Local Rings
Free Resolutions and Fitting Invariants
Duality, Canonical Modules, and Gorenstein Rings
Appendix 1 Field Theory
Appendix 2 Multilinear Algebra
Appendix 3 Homological Algebra
Appendix 4 A Sketch of Local Cohomology
Appendix 5 Category Theory
Appendix 6 Limits and Colimits
Appendix 7 Where Next?
Hints and Solutions for Selected Exercises
References
Index of Notation
Index

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