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Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) Paperback – March 1, 1999

ISBN-13: 978-0387942698 ISBN-10: 0387942696

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Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) + Algebraic Geometry (Graduate Texts in Mathematics) + Introduction To Commutative Algebra (Addison-Wesley Series in Mathematics)
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Product Details

  • Series: Graduate Texts in Mathematics (Book 150)
  • Paperback: 788 pages
  • Publisher: Springer (March 1, 1999)
  • Language: English
  • ISBN-10: 0387942696
  • ISBN-13: 978-0387942698
  • Product Dimensions: 9.2 x 6.1 x 1.7 inches
  • Shipping Weight: 2.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (13 customer reviews)
  • Amazon Best Sellers Rank: #271,560 in Books (See Top 100 in Books)

Editorial Reviews

Review

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


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Customer Reviews

People tend to have strong feelings about this book.
Alexander C. Zorach
If one is interested in taking on a thorough study of algebraic geometry, this book is a perfect starting point.
Dr. Lee D. Carlson
Most sections are fairly self-contained and many important topics are included in depth.
Michael Spertus

Most Helpful Customer Reviews

41 of 44 people found the following review helpful By Michael Spertus on July 27, 2000
Format: Paperback
This is often referred to as the standard text on commutative algebra.
It is an exceptionally good book on a subject that is normally difficult to get a handle on. Eisenbud's readable book gives intuitive and motivated proofs of even very technical results in commutative algebra, often illustrated with instructive examples, such as the useful figures illustrating embedded primes. A very nice feature is that he gives proofs to all the results in commutative algebra used by Robin Hartshorne's popular "Algebraic Geometry," making them a nice pair of books to read together.
I found this to be useful as a reference as well as a text. Most sections are fairly self-contained and many important topics are included in depth. I almost always find that it is the best place to learn any of the material covered.
This book belongs on the shelf of anyone learning algebraic geometry, although it will spend plenty of time off the shelf as well.
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40 of 45 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on September 3, 2001
Format: Paperback
If one is interested in taking on a thorough study of algebraic geometry, this book is a perfect starting point. The writing is excellent, and the student will find many exercises that illustrate and extend the results in each chapter. Readers are expected to have an undergraduate background in algebra, and maybe some analysis and elementary notions from differential geometry. Space does not permit a thorough review here, so just a brief summary of the places where the author has done an exceptional job of explaining or motivating a particular concept:
(1) The history of commutative algebra and its connection with algebraic geometry, for example the origin of the concept of an "ideal" of a ring as generalizing unique factorization.
(2) The discussion of the concept of localization, especially its origins in geometry. A zero dimensional ring (collection of "points") is a ring whose primes are all maximal, as expected.
(3) The theory of prime decomposition as a generalization of unique prime factorization. Primary decomposition is given a nice geometric interpretation in the book.
(4) Five different proofs of the Nullstellensatz discussed, giving the reader good insight on this important result.
(5) The geometric interpretation of an associated graded ring corresponding to the exceptional set in the blowup algebra.
(6) The notion of flatness of a module as a continuity of fibers and a test for this using the Tor functor.
(7) The characterization of Hensel's lemma as a version of Newton's method for solving equations. The geometric interpretation of the completion as representing the properties of a variety in neighborhoods smaller than Zariski open neighborhoods.
(8) The characterization of dimension using the Hilbert polynomial.
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14 of 17 people found the following review helpful By Alexander C. Zorach on December 16, 2007
Format: Paperback
People tend to have strong feelings about this book. In my opinion, the people who dislike it are those who expect it to be like a typical graduate-level math book. This book is extremely atypical for a math book; it's not meant to be read linearly, and the topics in it do not follow a typical logical dependency. Personally, I find it to be outstanding; my only complaint about it is that I wish there were more books like it!

Commutative algebra and algebraic geometry are extremely difficult subjects requiring a great deal of background. This book is written as a sort of intermediary text between introductory abstract algebra books with a full and exposition of algebraic structures, and advanced, highly technical texts that can be difficult to follow and grasp on a technical level. As such, this book focuses on developing intuition, and discussing the history and motivation behind the various mathematical structures presented. It assumes that most of the other aspects of the subject, including both the elementary expositions, and the more advanced technical details, can be found elsewhere (although, believe me, this book certainly has its share of both elementary expositions and advanced technical details!)

I think this book is actually better for self-study than for use as a textbook. Most of the people I have known who have used it as a textbook have been frustrated with it. Either way, it needs to be supplemented by other books. Personally, on algebra, I like the Dummit and Foote, Isaacs, and Lang books. Those three books have very little overlap with each other, and very little overlap with this book, and they offer a very useful difference of perspectives where they do overlap!
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6 of 7 people found the following review helpful By Daniel McLaury on July 6, 2012
Format: Paperback Verified Purchase
The text itself is great -- it fills in all the background Hartshorne inexplicably assumes you'll be familiar with in a clear and well-motivated way. You should definitely read it.

My low rating pertains specifically to the paperback binding. This book is 800 pages long, and despite being printed on what appears to be very thin paper the book is twice as thick as nearly any other book I own. The paperback binding simply isn't up to the task of holding the book together -- if you read anything that isn't in the middle couple of chapters, it develops permanent creases. I expect my copy will have fallen completely apart within a month or so.

Honestly, this book should have been split into two volumes or something, because the current size is absurdly unwieldy. As things stand, I'd recommend trying to find a hardcover or eBook edition.
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