Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- Chapter 1 Graded Rings and Modules
- Chapter 2 Filtrations and Noether Filtrations
- Chapter 3 The Theorems of Matijevic and Mori-Nagata
- Chapter 4 The Valuation Theorem
- Chapter 5 The Strong Valuation Theorem
- Chapter 6 Ideal Valuations (1)
- Chapter 7 Ideal Valuations (2)
- Chapter 8 The Multiplicity Function associated with a Filtration
- Chapter 9 The Degree Function of a Noether Filtration
- Chapter 10 The General Extension of a Local Ring
- Chapter 11 General Elements
- Chapter 12 Mixed Multiplicities and the Generalised Degree Formula
- Bibliography
- Index
- Index of Symbols
- Frontmatter
- Contents
- Preface
- Introduction
- Chapter 1 Graded Rings and Modules
- Chapter 2 Filtrations and Noether Filtrations
- Chapter 3 The Theorems of Matijevic and Mori-Nagata
- Chapter 4 The Valuation Theorem
- Chapter 5 The Strong Valuation Theorem
- Chapter 6 Ideal Valuations (1)
- Chapter 7 Ideal Valuations (2)
- Chapter 8 The Multiplicity Function associated with a Filtration
- Chapter 9 The Degree Function of a Noether Filtration
- Chapter 10 The General Extension of a Local Ring
- Chapter 11 General Elements
- Chapter 12 Mixed Multiplicities and the Generalised Degree Formula
- Bibliography
- Index
- Index of Symbols
Summary
The greater part of these notes were presented in the form of lectures during a visit to Nagoya University during the Winter of 1982–3. This visit was made possible by the support of the Japanese Ministry of Education and the British Council, and to both these bodies I would like to express my gratitude. My warmest thanks go to Professor Hideyuki Matsumura and his wife for their hospitality and the friendship they showed throughout my stay.
Coming closer to home, my thanks are also due to George Duller, Peter Vamos and the other members of the Mathematics Department of the University of Exeter for allowing me the use of a word processor. My thanks again to George Duller, and also to Tony Stratton, for the continual help and advice they have given me.
I also owe a debt of gratitude to the Cambridge University Press, particularly David Tranah, for advice throughout the preparation of the manuscript.
My thanks are also due to Professor Rodney Sharp, whose careful reading of the manuscript brought to light a great number of obscurities and errors which, I hope, have now been removed.
Finally, and not least, I thank my wife for her patience and her extraordinary ability as a proof-reader, and for a great deal more besides.
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- Lectures on the Asymptotic Theory of Ideals , pp. ix - xPublisher: Cambridge University PressPrint publication year: 1988