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Commutative Algebra : With View Toward Algebraic Geometry

Commutative Algebra : With View Toward Algebraic Geometry - 95 edition

ISBN13: 978-0387942698

Cover of Commutative Algebra : With View Toward Algebraic Geometry 95 (ISBN 978-0387942698)
ISBN13: 978-0387942698
ISBN10: 0387942696
Cover type:
Edition/Copyright: 95
Publisher: Springer-Verlag New York
Published: 1995
International: No

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Commutative Algebra : With View Toward Algebraic Geometry - 95 edition

ISBN13: 978-0387942698

David Eisenbud

ISBN13: 978-0387942698
ISBN10: 0387942696
Cover type:
Edition/Copyright: 95
Publisher: Springer-Verlag New York

Published: 1995
International: No
Summary

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.

Author Bio

Eisenbud, David : University of California

Table of Contents

Elemenary Definitions
Part I: Basic Constructions

Roots of Commutative Algebra
Localization
Associated Primes and Primary Decomposition
Integral Dependence and the Nullstellensatz
Filtrations and the Artin-Rees Lemma
Flat Families
Completion's and Hensel's Lemma

Part II: Dimension Theory

Fundemental Definitions of Dimensional Theory
The Principal Ideal Theorem and Systems of Parameters
Dimension and Codimension One
Dimension and Hilbert-Samuel Polynomials
The Dimension of Affine
Elimination Theory, Generic Freeness, and the Dimension of Fibers
Grobner Bases
Modules of Differentials

Part III: Homological Methods

Regular Sequences and the Koszul Complex
Depth, Codimension, and Cohen-Macaulay Rings
Homological Theory of Regular Local Rings
Resolutions and Fitting Invariants
Duality, Canonical Modules, and Gerstein Rings

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