Product Description

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.

Product Details

• Amazon Sales Rank: #567400 in Books
• Published on: 1999-03-01
• Original language: English
• Number of items: 1
• Binding: Paperback
• 797 pages

Customer Reviews

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.

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.