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Commutative Algebra

Overview

Authors:
  1. David Eisenbud

    1. Department of Mathematics, Brandeis University, Waltham, USA

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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.

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Table of contents (23 chapters)

  2. Introduction

  3. Elementary Definitions

  4. Basic Constructions

  5. Dimension Theory

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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

  • Department of Mathematics, Brandeis University, Waltham, USA

    David Eisenbud

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

  • 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

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