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The Theory Of Classical Valuations

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The Theory Of Classical Valuations

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Author : Paulo Ribenboim
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-05-21

The Theory Of Classical Valuations written by Paulo Ribenboim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-21 with Mathematics categories.

Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory. The presentation is fully up-to-date and will serve as a valuable resource for students and mathematicians.

The Theory Of Classical Valuations

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Author : Paulo Ribenboim
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

In his studies of cyclotomic fields, in view of establishing his monumental theorem about Fermat's last theorem, Kummer introduced "local" methods. They are concerned with divisibility of "ideal numbers" of cyclotomic fields by lambda = 1 - psi where psi is a primitive p-th root of 1 (p any odd prime). Henssel developed Kummer's ideas, constructed the field of p-adic numbers and proved the fundamental theorem known today. Kurschak formally introduced the concept of a valuation of a field, as being real valued functions on the set of non-zero elements of the field satisfying certain properties, like the p-adic valuations. Ostrowski, Hasse, Schmidt and others developed this theory and collectively, these topics form the primary focus of this book.

The Theory Of Valuations

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Author : Otto Franz Georg Schilling
language : en
Publisher: American Mathematical Soc.
Release Date : 1950-12-31

The Theory Of Valuations written by Otto Franz Georg Schilling and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950-12-31 with Mathematics categories.

Valuations Orderings And Milnor K Theory

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Author : Ido Efrat
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Valuations Orderings And Milnor K Theory written by Ido Efrat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

This monograph is a comprehensive exposition of the modern theory of valued and ordered fields. It presents the classical aspects of such fields: their arithmetic, topology, and Galois theory. Deeper cohomological aspects are studied in its last part in an elementary manner. This is done by means of the newly developed theory of generalized Milnor $K$-rings. The book emphasizes the close connections and interplay between valuations and orderings, and to a large extent, studies themin a unified manner. The presentation is almost entirely self-contained. In particular, the text develops the needed machinery of ordered abelian groups. This is then used throughout the text to replace the more classical techniques of commutative algebra. Likewise, the book provides an introductionto the Milnor $K$-theory. The reader is introduced to the valuation-theoretic techniques as used in modern Galois theory, especially in applications to birational anabelian geometry, where one needs to detect valuations from their ``cohomological footprints''. These powerful techniques are presented here for the first time in a unified and elementary way.

Ifs

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Author : W.L. Harper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Ifs written by W.L. Harper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

With publication of the present volume, The University of Western Ontario Series in Philosophy of Science enters its second phase. The first fourteen volumes in the Series were produced under the managing editorship of Professor James J. Leach, with the cooperation of a local editorial board. Many of these volumes resulted from colloguia and workshops held in con nection with the University of Western Ontario Graduate Programme in Philosophy of Science. Throughout its seven year history, the Series has been devoted to publication of high quality work in philosophy of science con sidered in its widest extent, including work in philosophy of the special sciences and history of the conceptual development of science. In future, this general editorial emphasis will be maintained, and hopefully, broadened to include important works by scholars working outside the local context. Appointment of a new managing editor, together with an expanded editorial board, brings with it the hope of an enlarged international presence for the Series. Serving the publication needs of those working in the various subfields within philosophy of science is a many-faceted operation. Thus in future the Series will continue to produce edited proceedings of worthwhile scholarly meetings and edited collections of seminal background papers. How ever, the publication priorities will shift emphasis to favour production of monographs in the various fields covered by the scope of the Series. THE MANAGING EDITOR vii W. L. Harper, R. Stalnaker, and G. Pearce (eds.), lIs, vii.

Valuation Theory And Its Applications

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Author : Franz-Viktor Kuhlmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-01-01

Valuation Theory And Its Applications written by Franz-Viktor Kuhlmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.

This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.

Valuation Approaches And Metrics

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Author : Aswath Damodaran
language : en
Publisher: Now Publishers Inc
Release Date : 2005

Valuation Approaches And Metrics written by Aswath Damodaran and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Business & Economics categories.

Valuation lies at the heart of much of what we do in finance, whether it is the study of market efficiency and questions about corporate governance or the comparison of different investment decision rules in capital budgeting. In this paper, we consider the theory and evidence on valuation approaches. We begin by surveying the literature on discounted cash flow valuation models, ranging from the first mentions of the dividend discount model to value stocks to the use of excess return models in more recent years. In the second part of the paper, we examine relative valuation models and, in particular, the use of multiples and comparables in valuation and evaluate whether relative valuation models yield more or less precise estimates of value than discounted cash flow models. In the final part of the paper, we set the stage for further research in valuation by noting the estimation challenges we face as companies globalize and become exposed to risk in multiple countries.

Reciprocity Laws

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Author : Franz Lemmermeyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-06

Reciprocity Laws written by Franz Lemmermeyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-06 with Mathematics categories.

This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

Integral Closure Of Ideals Rings And Modules

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Author : Craig Huneke
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-12

Integral Closure Of Ideals Rings And Modules written by Craig Huneke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-12 with Mathematics categories.

Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Geometric Aspects Of Functional Analysis

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Author : Vitali D. Milman
language : en
Publisher: Springer
Release Date : 2004-08-30

Geometric Aspects Of Functional Analysis written by Vitali D. Milman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-30 with Mathematics categories.

The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes. It reflects the general trends of the theory. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis. In addition the volume contains papers on related aspects of Probability, classical Convexity and also Partial Differential Equations and Banach Algebras. There are also two expository papers on topics which proved to be very much related to the main topic of the seminar. One is Statistical Learning Theory and the other is Models of Statistical Physics. All the papers of this collection are original research papers.

The Theory Of Classical Valuations

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