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Commutative algebra with view toward algebraic geometry

Author: David Eisenbud
Publisher: New York Berlin Heidelberg Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo Springer 1997
Series: Graduate texts in mathematics, 150
Edition/Format:   Print book : English
Summary:
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.
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: David Eisenbud
ISBN: 9783540942696 3540942696 9780387942698 0387942696 9780387942681 0387942688 3540942688 9783540942689
OCLC Number: 841233572
Notes: Literaturverz. S. 757 - 774
Description: XVI, 797 S. graph. Darst. 24 cm
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 Solutions for Selected Exercises; References; Index of Notations; Index
Series Title: Graduate texts in mathematics, 150
Responsibility: David Eisenbud

Abstract:

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  Read more...
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D. EisenbudCommutative 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 Read more...

 
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