Commutative Algebra by David Eisenbud, , 0387942696 Search discount cheap book, Compare Book prices, Find Lowest Price
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Commutative Algebra, cheap new, used books  Commutative Algebra: With a View Toward Algebraic Geometry (Graduate Texts in Mathematics): With a View Toward Algebraic Geometry (Graduate Texts in Mathematics)
Author: David Eisenbud  
ISBN: 0387942696   /   Paperback
Publisher: Springer-Verlag New York Inc.   /   1999-03-01
List Price: £30.50
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Customer Reviews:
A TEXTBOOK, in the best sense of the word     
Explains not only what the notions are, but also why were they singled out for study. Reading this book, we clearly see: 1. the complexity of the things we would like to understand, 2. the simplifications needed to get anywhere in our study, 3. technical theorems needed to operate with the notions we have defined. This is a great book because it shows how mathematics is done (not by Hilbert or Noether, but by the person reading the book). This is useful because we don't study mathematics just to look at the great results proved by others; we study it to see what is left unclear and how we could perhaps make improvements to our understanding of things.
Excellent on its own or next to Hartshorne     
First off, Eisenbud means for his book on commutative algebra to indicate many of the geometric notions that have helped shape the subject. He does this admirably--I found that in the first few chapters you can really learn some algebraic geometry. He also means for the course to be sufficient for reading through Robin Hartshorne's Algebraic Geometry. In fact, he has picked out the commutative algebra results Hartshorne uses (without proof) and made sure to give complete proofs of them in his book.

This being said, Eisenbud's book is also good for just plain learning some commutative algebra. His exposition flows very well and is extremely clear. He gives quite a few examples in text, and more are scattered in the exercises. Most of the exercises are not too difficult, but he has a few trickier ones (they are usually marked and include hints in the back). The book is huge, and has a huge breadth of scope (localisation, completions, homological methods, differentials, etc. are all in there). So, it also makes a useful reference. Plus, Eisenbud's point of view (a geometric one) allows the reader with a passing acquaintance with algebraic geometry to gain some insight into the constructions and methods of commutative algebra.

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