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Introduction To Commutative Algebra (Addison-Wesley Series in Mathematics) Paperback – February 21, 1994

ISBN-13: 978-0201407518 ISBN-10: 0201407515
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Product Details

  • Series: Addison-Wesley Series in Mathematics
  • Paperback: 138 pages
  • Publisher: Westview Press (February 21, 1994)
  • Language: English
  • ISBN-10: 0201407515
  • ISBN-13: 978-0201407518
  • Product Dimensions: 6 x 0.3 x 9 inches
  • Shipping Weight: 7.8 ounces (View shipping rates and policies)
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #189,444 in Books (See Top 100 in Books)

Customer Reviews

3.7 out of 5 stars
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32 of 33 people found the following review helpful By Pedro L. Ribeiro on October 16, 2001
Format: Paperback
Some people believe that, for getting into algebraic geometry (by this I mean Grothendieck-like AG, with schemes and all that), one needs a monolithic training in commutative algebra (something like both volumes of Zariski-Samuel, for example). I disagree. This little book seems to be specially suited to those who want to learn AG. It's a bit too brisk, specially at the beginning - if you don't already have an acquaintance with the basics of groups, rings and ideals, you may run into trouble - but very illuminating. Masterful choice of topics, great exercises (as a matter of fact, about half the topics of the book, and more specifically the ones that are directly related to AG, are treated in the exercises, some of them quite challenging) - like one said before, it looks like a "chapter 0" of Hartshorne's book on AG. The authors consciously estabilish relations between the commutative algebra and the modern foundations of AG over and over along the way, illuminating both topics.
For the algebra itself, it also gets on well with Rotman's "Galois Theory" and MacDonald's out-of-print introduction to AG, "Algebraic Geometry - Introduction to Schemes", besides being the perfect preamble in commutative algebra to the books of Mumford and Hartshorne. A gem.
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Format: Paperback
The strongest aspects of Atiyah & MacDonald's book are its brevity, accessibility to undergraduates, and subtle introduction of more advanced material.

Audience: I think an undergraduate with a solid understanding of material from a first course in abstract algebra (i.e., the chapter on rings--the modules chapter would help, but isn't necessary--from M. Artin's book 'Algebra' is more than sufficient) and some basic point-set topology from an intro real analysis course (or ch1-4 of Munkres) would be sufficient for fully appreciating the material. I think having experience in PS Topology is important for understanding parts of this book well; doing the exercises is possible if you learn it "on the fly," but I hadn't seen Urysohn's Lemma before, and even that caused me some "intuition" hangups; to fully appreciate the material, I would recommend doing a healthy number of problems in topology first.

Material: The material uses concepts from homological algebra, though in a disguised form; students with experience in category theory will find offhanded comments that recast some of the material in that language, but CT is absolutely not essential to understand the material well. It also provides exercises that lead naturally into topics from Algebraic Geometry and Algebraic Number Theory quite readily; a nice set of problems in CH1 walk a student through construction of the Zariski topology, prime spectrum, etc., and some functional properties of morphisms between spectra. Algebraic Number Theory starts showing up after chapter 4 in greater detail, and would lead comfortably into Lang's GTM on ALNT by CH9 (though I only read a bit of Lang, the first chapter felt natural).
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19 of 21 people found the following review helpful By A Customer on February 8, 1999
Format: Paperback
This book is almost everything you need to gain a solid background in commutative algebra. Moreover, it's trimmed down enough so that it doesn't have the things you don't need. If you're not an algebraic geometer or number theorist, it may be the only commutative algebra book you'll need.
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23 of 27 people found the following review helpful By A Customer on April 20, 1999
Format: Paperback
This is how mathematics texts SHOULD be written. As in technical writing, the smaller text is the better written text. Everything is clean and direct, with clairity obviously a prime consideration. One never gets mired down. The proofs are always as close to a "THE BOOK" proof as possible, with illuminating examples, and plenty of excercises, many with outlines for solution, which makes the book ideal for self study. This book is a revelation. If I had to take only one math text with me to a desert island, this would be the one.
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12 of 13 people found the following review helpful By A Mathematician on February 2, 2008
Format: Paperback
This book is what led to me getting a Ph.D. in commutative algebra. I carried it around for an entire summer studying it. I highly recommend it for a graduate student introduction to the subject, after taking a course that at least introduces modules. Too bad there wasn't a volume II.
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6 of 6 people found the following review helpful By mathwonk on April 12, 2012
Format: Paperback
This is a very good, short and useful account of basic commutative algebra, by two famous algebraic geometers (one a Fields medalist) that has long been recommended as unusually accessible to students. Unfortunately such books have been shamelessly inflated in price in recent years, and I for one agree that this book's price has now exceeded its value. It is after all, an outline of material explained in more detail elsewhere, and it would be an unusually well off student who can be recommended to choose this book at this price. For about the same money one can buy both of Miles Reid's books, Undergraduate commutative algebra, and Undergraduate algebraic geometry, and probably be better off, or the very well regarded second attempt at explaining the topic by Matsumura, Commutative ring theory. Eisenbud's massive tome at over 5 times the length is now about half as expensive, at around $35. Even Hartshorne's standard algebraic geometry book, which at least states all the commutative algebra results needed, is cheaper. I regret to say this since the book really is a good one, but the authors are being embarrassed and their students are being exploited here by this pricing policy. One should not encourage this kind of blackmail by publishers. In fact I just noticed the classic work by Zariski and Samuel is available used for $50 or less for both volumes! Last time I taught the course I found myself preferring that fuller version to the one under review. I suggest going there instead.
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Introduction To Commutative Algebra (Addison-Wesley Series in Mathematics)
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