Lectures on the Asymptotic Theory of Ideals

By: D. Rees, J. W. S. Cassels (Editor), N. J. Hitchin (Editor)

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Paperback | 17 April 1989

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216 Pages

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In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work is an expansion of lectures given at Nagoya University.

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Non-Fiction Mathematics Algebra

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Non-Fiction Mathematics Algebra

Preface
Introduction
Graded rings and modules
Filtrations and noether filtrations
The theorems of matijevic and mori-nagata
The valuation theorem
The strong valuation theorem
Ideal valuations (1)
Ideal valuations (2)
The multiplicity function associated with a filtration
The degree function of a noether filtration
The general extension of a local ring
General elements
Mixed multiplicities and the generalised degree formula
Bibliography
Index
Index of symbols
Table of Contents provided by Publisher. All Rights Reserved.

Lectures on the Asymptotic Theory of Ideals

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