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Klappentext 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. Zusammenfassung This work 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. Inhaltsverzeichnis Preface; Introduction; 1. Graded rings and modules; 2. Filtrations and noether filtrations; 3. The theorems of matijevic and mori-nagata; 4. The valuation theorem; 5. The strong valuation theorem; 6. Ideal valuations (1); 7. Ideal valuations (2); 8. The multiplicity function associated with a filtration; 9. The degree function of a noether filtration; 10. The general extension of a local ring; 11. General elements; 12. Mixed multiplicities and the generalised degree formula; Bibliography; Index; Index of symbols.
