Commutative algebra with a view toward algebraic geometry

David Eisenbud

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.

「Nielsen BookData」より

[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

「Nielsen BookData」より

この本の情報

書名 Commutative algebra with a view toward algebraic geometry
著作者等 Eisenbud, David
シリーズ名 Graduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1995
版表示 1st ed. 1995. Corr. 3rd printing 1999
ページ数 xvi, 785 p.
大きさ 25 cm
ISBN 0387942696
3540942688
3540942696
0387942688
NCID BA24865452
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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