Commutative Algebra: With a View Toward Algebraic Geometry

Commutative Algebra: With a View Toward Algebraic Geometry

Paperback Graduate Texts in Mathematics

By (author) David Eisenbud

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  • Publisher: Springer-Verlag New York Inc.
  • Format: Paperback | 804 pages
  • Dimensions: 155mm x 234mm x 46mm | 1,134g
  • Publication date: 1 March 1999
  • Publication City/Country: New York, NY
  • ISBN 10: 0387942696
  • ISBN 13: 9780387942698
  • Edition statement: 1st ed. 1995. Corr. 3rd printing 1999
  • Illustrations note: biography
  • Sales rank: 340,002

Product description

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

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Review quote

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

Table of contents

Introduction; 0. Elementary Definitions; I. Basic Constructions; 1. Roots and Commutative Algebra; 2. Localization; 3. Associated Primes and Primary Decomposition; 4. Integral Dependence and the Nullstellensatz; 5. Filtrations and the Artin-Rees Lemma; 6. Flat Families; 7. Completions and Hensel's Lemma; II. Dimension Theory; 8. Introduction to Dimension Theory; 9. Fundamental Definitions of Dimension Theory; 10. The Principal Ideal Theorem and Systems of Parameters; 11. Dimension and Codimension One; 12. Dimension and Hilbert- Samuel Polynomials; 13. Dimension of Affine Rings; 14. Elimination Theory, Generic Freeness and the Dimension of Fibers; 15. Grobner Bases; 16. Modules of Differentials; III. Homological Methods; 17. Regular Sequence and the Koszul Complex; 18. Depth, Codimension and Cohen-Macaulay Rings; 19. Homological Theory of Regular Local Rings; 20. Free Resolutions and Fitting Invariants; 21. 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