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| Medienart: | Internetquelle |
|---|---|
| Dokumenttyp | Buch, Internet-Ressource |
| Alle Autoren: |
David Eisenbud |
| ISBN: | 9783540942696 3540942696 9780387942698 0387942696 9780387942681 0387942688 3540942688 9783540942689 |
| OCLC-Nummer: | 841233572 |
| Anmerkungen: | Literaturverz. S. 757 - 774 |
| Beschreibung: | XVI, 797 S. graph. Darst. 24 cm |
| Inhalt: | 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 |
| Serientitel: | Graduate texts in mathematics, 150 |
| Verfasserangabe: | 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
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