Commutative Algebra : With a View Toward Algebraic Geometry

With a View Toward Algebraic Geometry

By: J. H. Ewing, David Eisenbud, F. W. Gehring (As told to)

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Paperback | 1 February 1999

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820 Pages

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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.

Industry Reviews

D. Eisenbud

Commutative Algebra with a View Toward Algebraic Geometry

"This text has personality--Those 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

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Non-Fiction Mathematics Algebra Geometry Algebraic Geometry Groups & Group Theory

Introduction	p. 1
Elementary Definitions	p. 11
Roots of Commutative Algebra	p. 21
Localization	p. 57
Associated Primes and Primary Decomposition	p. 87
Integral Dependence and the Nullstellensatz	p. 117
Filtrations and the Artin-Rees Lemma	p. 145
Flat Families	p. 155
Completions and Hensel's Lemma	p. 179
Introduction to Dimension Theory	p. 213
Fundamental Definitions of Dimension Theory	p. 225
The Principal Ideal Theorem and Systems of Parameters	p. 231
Dimension and Codimension One	p. 247
Dimension and Hilbert-Samuel Polynomials	p. 271
The Dimension of Affine Rings	p. 281
Elimination Theory, Generic Freeness, and the Dimension of Fibers	p. 303
Grobner Bases	p. 317
Modules of Differentials	p. 383
Regular Sequences and the Koszul Complex	p. 419
Depth, Codimension, and Cohen-Macaulay Rings	p. 447
Homological Theory of Regular Local Rings	p. 469
Free Resolutions and Fitting Invariants	p. 489
Duality, Canonical Modules, and Gorenstein Rings	p. 519
Appendix 1 Field Theory	p. 555
Appendix 2 Multilinear Algebra	p. 565
Appendix 3 Homological Algebra	p. 611
Appendix 4 A Sketch of Local Cohomology	p. 683
Appendix 5 Category Theory	p. 689
Appendix 6 Limits and Colimits	p. 697
Appendix 7 Where Next?	p. 708
Hints and Solutions for Selected Exercises	p. 711
References	p. 745
Index of Notation	p. 763
Index	p. 767
Table of Contents provided by Blackwell. All Rights Reserved.

Commutative Algebra : With a View Toward Algebraic Geometry

With a View Toward Algebraic Geometry

At a Glance

Paperback

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