Commutative Ring Theory (Cambridge Studies in Advanced Mathematics) | 
 enlarge | Author: H. Matsumura
Creator: Miles Reid
Publisher: Cambridge University Press
Category: Book
List Price: $65.00
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Rating:  2 reviews
Sales Rank: 316393
Media: Paperback
Pages: 336
Number Of Items: 1
Shipping Weight (lbs): 1
Dimensions (in): 8.8 x 6 x 0.7
ISBN: 0521367646
Dewey Decimal Number: 512
EAN: 9780521367646
Publication Date: June 30, 1989
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Condition: Brand new item. Over 3.5 million customers served. Order now. Selling online since 1995. Few left in stock - order soon. Code: C20080902203241B
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Product Description
In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially self-contained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book.
Book Description
Commutative ring theory is important as a foundation for algebraic and complex analytical geometry and this text covers the basic material with a solid knowledge of modern algebra as the only prerequisite.
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| Customer Reviews:
Truly Beautiful April 28, 2000
29 out of 30 found this review helpful
Matsumura has achieved a great success with this book. The first nine chapters contain all of the algebra used in Hartshorne's _Algebraic Geometry_, and a reader who masters all of that material will be well on the way to a solid understanding of algebraic geometry. At the same time, the writing is clear and concise, and the exercises (which the reader should of course do!) are enlightening. In this regard, one should compare Matsumura's book with Eisenbud's _Commutative Algebra with a View Toward Algebraic Geometry_, which has a similar scope but takes up 800 pages. Both books are beautifully written, but while Matsumura prefers a more subtle way of teaching the reader the tricks of the trade, Eisenbud makes explicit commentary on his methods and intuition. Another helpful comparison between the two is in their fundamental approach: Matsumura tends to use universal constructions which are not computationally effective, while Eisenbud seems to keep the computer in mind. Thus, whereas Eisenbud studies the module of differentials using generators and relations, Matsumura uses the universal properties of representable functors.Unfortunately, this book is not sufficient for a first introduction to commutative algebra, as the pace can be brisk for a reader without the mathematical maturity to appreciate Matsumura's condensed style. (One could read this book after reading Atiyah and MacDonald's _Introduction to Commutative Algebra_.) Nevertheless, for a reader seeking a solid understanding of the commutative algebra necessary for (modern) algebraic geometry, there is no better reference than Matsumura's book. A minor gripe: the formatting is visually slightly confusing -- the announcements of Theorems, Corollaries, Lemmas, Remarks, Proofs, etc. are all set in italic typeface, so there is not much to orient the eye on the page.
great text for graduate intro to comm. alg. December 17, 2006
Knight W. Fu (USA)
3 out of 3 found this review helpful
A great transition from elementary to advanced comm. ring theory: goes into greater details than Reid's Undergrad Comm. Alg. and Atiyah-MacDonald's Intro. to Comm. Alg. The proofs are clear and concise and the text is well-organized.
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