Commutative Algebra with a View Toward Algebraic Geometry

Name: Commutative Algebra with a View Toward Algebraic Geometry
Price: 40.76 USD
Availability: InStock
ISBN: 9780387942698

ISBN-10: 0387942696

ISBN-13: 9780387942698

Edition: 1995

Authors: David Eisenbud

List price: $49.95

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Description:

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text.One novel feature is a chapter devoted to a quick but…

Book details

List price: $49.95
Copyright year: 1995
Publisher: Springer New York
Publication date: 3/30/1995
Binding: Paperback
Pages: 800
Size: 6.10" wide x 9.25" long x 0.57" tall
Weight: 2.860
Language: English



Introduction


Elementary Definitions



Roots of Commutative Algebra



Localization



Associated Primes and Primary Decomposition



Integral Dependence and the Nullstellensatz



Filtrations and the Artin-Rees Lemma



Flat Families



Completions and Hensel's Lemma



Introduction to Dimension Theory



Fundamental Definitions of Dimension Theory



The Principal Ideal Theorem and Systems of Parameters



Dimension and Codimension One



Dimension and Hilbert-Samuel Polynomials



The Dimension of Affine Rings



Elimination Theory, Generic Freeness, and the Dimension of Fibers



Grobner Bases



Modules of Differentials



Regular Sequences and the Koszul Complex



Depth, Codimension, and Cohen-Macaulay Rings



Homological Theory of Regular Local Rings



Free Resolutions and Fitting Invariants



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 Notation


Index