Commutative algebra with a view toward algebraic geometry

著者

書誌事項

Commutative algebra with a view toward algebraic geometry

David Eisenbud

（Graduate texts in mathematics, v. 150）

Springer-Verlag, c1995

  • : hd : us
  • : hd : gw
  • : pbk : us
  • : pbk : gw

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注記

Includes bibliographical references (p. [745]-762), index of notation, and index

内容説明・目次

巻冊次

: hd : us ISBN 9780387942681

内容説明

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.

目次

  • 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
巻冊次

: pbk : us ISBN 9780387942698

内容説明

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.

目次

  • 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
巻冊次

: hd : gw ISBN 9783540942689

内容説明

This book is an attempt to write on commutative algebra in a way that includes the geometric ideas that played a great role in its formation; with a view, in short, towards Algebraic Geometry. The author provides a book that covers the material that graduate students studying Algebraic Geometry - and in particular those studying the book Algebraic Geometry by Robin Hartshorne - should know. The reader should have had one year of basic graduate algebra.
巻冊次

: pbk : gw ISBN 9783540942696

内容説明

This book is an attempt to write on commutative algebra in a way that includes the geometric ideas that played a great role in its formation with a view, in short, towards algebraic geometry. The author provides a book that covers the material that graduate students studying algebraic geometry - and in particular those studying, "Algebraic Geometry" by Robin Hartshorne - should know. The reader should have had had one year of basic graduate algebra.

目次

Introduction.- Elementary Definitions.- I Basic Constructions.- II Dimension Theory.- III Homological Methods.- Appendices.- Hints and Solutions for Selected Exercises.- References.- Index of Notation.- Index.

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