Introduction To Commutative Algebra [Paperback]

Michael Atiyah (Author)

Book Description

ISBN-10: 0201407515 | ISBN-13: 978-0201407518 | Publication Date: February 21, 1994

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

Product Details

• Paperback: 138 pages
• Publisher: Westview Press (February 21, 1994)
• Language: English
• ISBN-10: 0201407515
• ISBN-13: 978-0201407518
• Product Dimensions: 8.8 x 6 x 0.5 inches
• Shipping Weight: 7.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #140,284 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

28 of 29 people found the following review helpful:

5.0 out of 5 stars A baptism of fire for Algebraic Geometry, October 16, 2001

By 

Pedro L. Ribeiro "lqp-man" (Cotia, SP Brazil) - See all my reviews
(REAL NAME)   

This review is from: Introduction To Commutative Algebra (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.

16 of 16 people found the following review helpful:

4.0 out of 5 stars A pocket guide to algebra, February 8, 1999

By A Customer

This review is from: Introduction To Commutative Algebra (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.

22 of 24 people found the following review helpful:

5.0 out of 5 stars A gem of mathematical writing, April 20, 1999

By A Customer

This review is from: Introduction To Commutative Algebra (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.