Commutative Algebra With a View Toward Algebraic Geometry 1st edition by David Eisenbud 9781461253501 1461253500

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ISBN 10: 1461253500
ISBN 13: 9781461253501 
Author: David Eisenbud

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.

Commutative Algebra With a View Toward Algebraic Geometry 1st Table of contents:

1. Introduction
2. Elementary Definitions
3. Basic Constructions
4. Roots of Commutative Algebra
5. Localization
6. Associated Primes and Primary Decomposition
7. Integral Dependence and the Nullstellensatz
8. Filtrations and the Artin-Rees Lemma
9. Flat Families
10. Completions and Hensel’s Lemma
11. Dimension Theory
12. Introduction to Dimension Theory
13. Fundamental Definitions of Dimension Theory
14. The Principal Ideal Theorem and Systems of Parameters
15. Dimension and Codimension One
16. Dimension and Hilbert-Samuel Polynomials
17. The Dimension of Affine Rings
18. Elimination Theory, Generic Freeness, and the Dimension of Fibers
19. Gröbner Bases

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