The Theory Of Classical Valuations

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 407 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205517

Get Book

The Theory of Classical Valuations by Paulo Ribenboim Pdf

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.

Author : Otto Franz Georg Schilling
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 43,7 Mb
Release : 1950-12-31
Category : Mathematics
ISBN : 9780821815045

Get Book

The Theory of Valuations by Otto Franz Georg Schilling Pdf

Author : Hidetoshi Marubayashi,Fred Van Oystaeyen
Publisher : Springer
Page : 225 pages
File Size : 49,6 Mb
Release : 2012-08-21
Category : Mathematics
ISBN : 9783642311529

Get Book

Prime Divisors and Noncommutative Valuation Theory by Hidetoshi Marubayashi,Fred Van Oystaeyen Pdf

Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simple algebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras. Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized algebras, the development of a theory of Hopf valuations on Hopf algebras and quantum groups, noncommutative valuations on the Weyl field and interesting rings of invariants and valuations of Gauss extensions.

Author : Ido Efrat
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 52,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821840412

Get Book

Valuations, Orderings, and Milnor $K$-Theory by Ido Efrat Pdf

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.

Author : Franz-Viktor Kuhlmann,Salma Kuhlmann,Murray Marshall
Publisher : American Mathematical Soc.
Page : 470 pages
File Size : 51,8 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0821871390

Get Book

Valuation Theory and Its Applications by Franz-Viktor Kuhlmann,Salma Kuhlmann,Murray Marshall Pdf

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.

Author : Antonio Campillo
Publisher : Erich Schmidt Verlag GmbH & Co. KG
Page : 674 pages
File Size : 46,7 Mb
Release : 2014
Category : Galois theory
ISBN : 303719149X

Get Book

Valuation Theory in Interaction by Antonio Campillo Pdf

For more than a century, valuation theory has had its classical roots in algebraic number theory, algebraic geometry and the theory of ordered fields and groups. In recent decades it has seen an amazing expansion into many other areas. Moreover, having been dormant for a while in algebraic geometry, it has now been reintroduced as a tool to attack the open problem of resolution of singularities in positive characteristic and to analyze the structure of singularities. Driven by this topic, and by its many new applications in other areas, the research in valuation theory itself has also been intensified, with a particular emphasis on the deep open problems in positive characteristic. The multifaceted development of valuation theory has been monitored by two International Conferences and Workshops: the first in 1999 in Saskatoon, Canada, and the second in 2011 in Segovia and El Escorial in Spain. This book grew out of the second conference and presents high quality papers on recent research together with survey papers that illustrate the state of the art in several areas and applications of valuation theory. This book is addressed to researchers and graduate students who work in valuation theory or the areas where it is applied, as well as a general mathematical audience interested in the expansion and usefulness of the valuation theoretical approach, which has been called the ``most analytic'' form of algebraic reasoning. For young mathematicians who want to enter these areas of research, it provides a valuable source of up-to-date information.

Author : Semyon Alesker
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 47,5 Mb
Release : 2018-06-27
Category : Graph labelings
ISBN : 9781470443597

Get Book

Introduction to the Theory of Valuations by Semyon Alesker Pdf

Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the Klain-Schneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent developments in the theory of translation-invariant continuous valuations, some of which turn out to be useful in integral geometry. This book grew out of lectures that were given in August 2015 at Kent State University in the framework of the NSF CBMS conference “Introduction to the Theory of Valuations on Convex Sets”. Only a basic background in general convexity is assumed.

Author : Otto Endler
Publisher : Unknown
Page : 256 pages
File Size : 44,8 Mb
Release : 1972-12-06
Category : Electronic
ISBN : 3642655068

Get Book

Valuation Theory by Otto Endler Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,6 Mb
Release : 2014
Category : Electronic
ISBN : 3037196491

Get Book

Valuation Theory in Interaction by Anonim Pdf

Author : Manfred Knebusch,Tobias Kaiser
Publisher : Springer
Page : 202 pages
File Size : 54,5 Mb
Release : 2014-03-20
Category : Mathematics
ISBN : 9783319032122

Get Book

Manis Valuations and Prüfer Extensions II by Manfred Knebusch,Tobias Kaiser Pdf

This volume is a sequel to “Manis Valuation and Prüfer Extensions I,” LNM1791. The Prüfer extensions of a commutative ring A are roughly those commutative ring extensions R / A, where commutative algebra is governed by Manis valuations on R with integral values on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Gräter’s work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called “Kronecker extensions,” where PM valuations are put to use in arbitrary commutative ring extensions in a way that ultimately goes back to the work of Leopold Kronecker.

Author : Semyon Alesker,Joseph H.G. Fu
Publisher : Springer
Page : 121 pages
File Size : 51,7 Mb
Release : 2014-10-09
Category : Mathematics
ISBN : 9783034808743

Get Book

Integral Geometry and Valuations by Semyon Alesker,Joseph H.G. Fu Pdf

In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, provides an introduction to the theory of convex valuations with emphasis on recent developments. In particular, it presents the new structures on the space of valuations discovered after Alesker's irreducibility theorem. The newly developed theory of valuations on manifolds is also described. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló. The approach is new and based on the notions and tools presented in the first part. This original viewpoint not only enlightens the classical integral geometry of euclidean space, but it also allows the computation of kinematic formulas in other geometries, such as hermitian spaces. The book will appeal to graduate students and interested researchers from related fields including convex, stochastic, and differential geometry. ​

Author : W.L. Harper,G.A. Pearce,R. Stalnaker
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400991170

Get Book

IFS by W.L. Harper,G.A. Pearce,R. Stalnaker Pdf

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.

Author : E. Agazzi
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789400990562

Get Book

Modern Logic — A Survey by E. Agazzi Pdf

Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recom prehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be con sidered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a diSCipline, is that one has succeeded in isolating the 'scientific core' of it, by restricting the somehow vague and redundant generality of its original 'philosophical' configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By follOwing this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition.

Author : Franz-Viktor Kuhlmann
Publisher : Unknown
Page : 0 pages
File Size : 52,9 Mb
Release : 2002
Category : Valuation theory
ISBN : 1470430665

Get Book

Valuation Theory and Its Applications by Franz-Viktor Kuhlmann Pdf

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). The special feature of this book is its focus on current applications of valuation theory to a broad range of topics. This first volume contains research and survey papers on a variety of valuation-theoretic topics, including rigid analytic geometry, real algebraic geometry, resolution of singularities, noncommutative valuation theory, valuations on fields, and Galois theory. Also included is a paper on the.

Author : J. Alajbegovic,J. Mockor
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401127165

Get Book

Approximation Theorems in Commutative Algebra by J. Alajbegovic,J. Mockor Pdf

Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc. Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups. Part II investigates approximation theorems from a general, categorical point of view. This part is essentially self-contained and requires only a basic knowledge of category theory and first-order logic. For researchers and graduate students of commutative algebra, category theory, as well as applications of logic.