Commutative Ring Theory

Klappentext This book explores commutative ring theory! an important a foundation for algebraic geometry and complex analytical geometry. Zusammenfassung 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. Inhaltsverzeichnis 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.

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


Zusammenfassung
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.

Inhalt
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.

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