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Commutative Algebra : With a View Toward Algebraic Geometry :  With a View Toward Algebraic Geometry - David Eisenbud

Commutative Algebra : With a View Toward Algebraic Geometry

With a View Toward Algebraic Geometry


Published: February 1999
Ships: 15 business days
15 business days

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.

D. Eisenbud

Commutative Algebra with a View Toward Algebraic Geometry

"This text has personalityThose familiar with Eisenbud"s own research will recognize its traces in his choice of topics and manner of approach. The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible."MATHEMATICAL REVIEWS

Introductionp. 1
Elementary Definitionsp. 11
Roots of Commutative Algebrap. 21
Localizationp. 57
Associated Primes and Primary Decompositionp. 87
Integral Dependence and the Nullstellensatzp. 117
Filtrations and the Artin-Rees Lemmap. 145
Flat Familiesp. 155
Completions and Hensel's Lemmap. 179
Introduction to Dimension Theoryp. 213
Fundamental Definitions of Dimension Theoryp. 225
The Principal Ideal Theorem and Systems of Parametersp. 231
Dimension and Codimension Onep. 247
Dimension and Hilbert-Samuel Polynomialsp. 271
The Dimension of Affine Ringsp. 281
Elimination Theory, Generic Freeness, and the Dimension of Fibersp. 303
Grobner Basesp. 317
Modules of Differentialsp. 383
Regular Sequences and the Koszul Complexp. 419
Depth, Codimension, and Cohen-Macaulay Ringsp. 447
Homological Theory of Regular Local Ringsp. 469
Free Resolutions and Fitting Invariantsp. 489
Duality, Canonical Modules, and Gorenstein Ringsp. 519
Appendix 1 Field Theoryp. 555
Appendix 2 Multilinear Algebrap. 565
Appendix 3 Homological Algebrap. 611
Appendix 4 A Sketch of Local Cohomologyp. 683
Appendix 5 Category Theoryp. 689
Appendix 6 Limits and Colimitsp. 697
Appendix 7 Where Next?p. 708
Hints and Solutions for Selected Exercisesp. 711
Referencesp. 745
Index of Notationp. 763
Indexp. 767
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387942698
ISBN-10: 0387942696
Series: Graduate Texts in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 800
Published: February 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.6 x 16.5  x 4.2
Weight (kg): 1.2