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Table of contents (23 chapters)
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Front Matter
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Introduction
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Elementary Definitions
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Dimension Theory
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Front Matter
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Keywords
About this book
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 thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.
Reviews
D. Eisenbud
Commutative 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 of approach. The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible."—MATHEMATICAL REVIEWS
Authors and Affiliations
Bibliographic Information
Book Title: Commutative Algebra
Book Subtitle: with a View Toward Algebraic Geometry
Authors: David Eisenbud
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-5350-1
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1995
Hardcover ISBN: 978-0-387-94268-1Published: 30 March 1995
Softcover ISBN: 978-0-387-94269-8Published: 30 March 1995
eBook ISBN: 978-1-4612-5350-1Published: 01 December 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVI, 800
Topics: Algebraic Geometry