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Commutative algebra with view toward algebraic geometry

Autor: David Eisenbud
Editora: New York Berlin Heidelberg Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo Springer 1997
Séries: Graduate texts in mathematics, 150
Edição/Formato   Imprimir livro : Inglês
Resumo:
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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Detalhes

Tipo de Material: Recurso Internet
Tipo de Documento Livro, Recursos de internet
Todos os Autores / Contribuintes: David Eisenbud
ISBN: 9783540942696 3540942696 9780387942698 0387942696 9780387942681 0387942688 3540942688 9783540942689
Número OCLC: 841233572
Notas: Literaturverz. S. 757 - 774
Descrição: XVI, 797 S. graph. Darst. 24 cm
Conteúdos: 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
Título da Série: Graduate texts in mathematics, 150
Responsabilidade: David Eisenbud

Resumo:

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  Ler mais...
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Nielsen BookData

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 Ler mais...

 
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