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Cambridge Studies in Advanced Mathematics #8: Commutative Ring Theory

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Cambridge Studies in Advanced Mathematics #8: Commutative Ring Theory Cover

 

Synopses & Reviews

Publisher Comments:

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 News Annotation:

Graduate textbook for students in commutative algebra covering dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings, and valuation rings. Exercises.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

Synopsis:

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.

Table of Contents

Preface; Introduction; Conventions and terminology; 1. Commutative rings and modules; 2. prime ideals; 3. Properties of extension rings; 4. Valuation rings; 5. Dimension theory; 6. Regular sequences; 7. Regular rings; 8. Flatness revisited; 9. Derivations; 10. I-smoothness; 11. Applications of complete local rings; Appendices; References; Index.

Product Details

ISBN:
9780521367646
Editor:
Bollobas, B.
Publisher:
Cambridge University Press
Editor:
Bollobas, B.
Editor:
Bollobas, Bela
Author:
Fulton, W.
Author:
Sarnak, P.
Author:
Kirwan, F.
Author:
Matsumura, Hideyuki
Author:
Katok, A.
Author:
Matsumura, H.
Author:
Bollobas, B.
Author:
Reid, Miles
Location:
Cambridge
Subject:
Algebra - General
Subject:
Commutative rings
Subject:
Mathematics - Algebra
Edition Number:
1
Edition Description:
Trade paper
Series:
Cambridge Studies in Advanced Mathematics (Paperback)
Series Volume:
8
Publication Date:
20081031
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Pages:
336
Dimensions:
9.00x6.01x.71 in. 1.00 lbs.

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Related Subjects

History and Social Science » World History » General
Science and Mathematics » Mathematics » Algebra » General

Cambridge Studies in Advanced Mathematics #8: Commutative Ring Theory New Trade Paper
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$94.25 In Stock
Product details 336 pages Cambridge University Press - English 9780521367646 Reviews:
"Synopsis" by , This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
"Synopsis" by , 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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