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Commutative Ring Theory H. Matsumura

Commutative Ring Theory By H. Matsumura

Commutative Ring Theory by H. Matsumura


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Summary

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.

Commutative Ring Theory Summary

Commutative Ring Theory by H. Matsumura

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.

Commutative Ring Theory Reviews

...an absolutely essential companion to researchers in commutative algebra and an important reference for those in neighboring fields. American Scientist

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.

Additional information

NLS9780521367646
9780521367646
0521367646
Commutative Ring Theory by H. Matsumura
New
Paperback
Cambridge University Press
1989-05-25
336
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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