Valued Fields

Valued Fields
Author: Antonio J. Engler
Publisher: Springer Science & Business Media
Total Pages: 210
Release: 2005-12-28
Genre: Mathematics
ISBN: 354030035X

Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.

Multi-Valued Fields

Multi-Valued Fields
Author: Yuri L. Ershov
Publisher: Springer Science & Business Media
Total Pages: 286
Release: 2001-08-31
Genre: Mathematics
ISBN: 9780306110689

For more than 30 years, the author has studied the model-theoretic aspects of the theory of valued fields and multi-valued fields. Many of the key results included in this book were obtained by the author whilst preparing the manuscript. Thus the unique overview of the theory, as developed in the book, has been previously unavailable. The book deals with the theory of valued fields and mutli-valued fields. The theory of Prüfer rings is discussed from the `geometric' point of view. The author shows that by introducing the Zariski topology on families of valuation rings, it is possible to distinguish two important subfamilies of Prüfer rings that correspond to Boolean and near Boolean families of valuation rings. Also, algebraic and model-theoretic properties of multi-valued fields with near Boolean families of valuation rings satisfying the local-global principle are studied. It is important that this principle is elementary, i.e., it can be expressed in the language of predicate calculus. The most important results obtained in the book include a criterion for the elementarity of an embedding of a multi-valued field and a criterion for the elementary equivalence for multi-valued fields from the class defined by the additional natural elementary conditions (absolute unramification, maximality and almost continuity of local elementary properties). The book concludes with a brief chapter discussing the bibliographic references available on the material presented, and a short history of the major developments within the field.

Sequence Spaces and Summability over Valued Fields

Sequence Spaces and Summability over Valued Fields
Author: P. N. Natarajan
Publisher: CRC Press
Total Pages: 169
Release: 2019-07-09
Genre: Mathematics
ISBN: 1000074919

Sequence spaces and summability over valued fields is a research book aimed at research scholars, graduate students and teachers with an interest in Summability Theory both Classical (Archimedean) and Ultrametric (non-Archimedean). The book presents theory and methods in the chosen topic, spread over 8 chapters that seem to be important at research level in a still developing topic. Key Features Presented in a self-contained manner Provides examples and counterexamples in the relevant contexts Provides extensive references at the end of each chapter to enable the reader to do further research in the topic Presented in the same book, a comparative study of Archimedean and non-Archimedean Summability Theory Appeals to young researchers and experienced mathematicians who wish to explore new areas in Summability Theory The book is written by a very experienced educator and researcher in Mathematical Analysis particularly Summability Theory.

Bounds on Transfer Principles for Algebraically Closed and Complete Discretely Valued Fields

Bounds on Transfer Principles for Algebraically Closed and Complete Discretely Valued Fields
Author: Scott Shorey Brown
Publisher: American Mathematical Soc.
Total Pages: 100
Release: 1978
Genre: Mathematics
ISBN: 0821822047

We study the replacement of quantifiers in statements about algebraically closed fields or complete discretely valued fields with residue class field [italic]Z[italic subscript]p and p large compared to the length of the statement, by quantifiers which range over finite sets of algebraic numbers. Since these algebraic numbers may be effectively determined and manipulated, this gives decision procedures in these cases.

Alison Balter's Mastering Microsoft Office Access 2007 Development

Alison Balter's Mastering Microsoft Office Access 2007 Development
Author: Alison Balter
Publisher: Pearson Education
Total Pages: 1766
Release: 2007-05-31
Genre: Computers
ISBN: 0132715163

Microsoft Office 2007 is a major upgrade from the last version of Office; Access will also be greatly revised. Alison Balter is the name that Access developers will trust to guide them through Access 2007's new features. She has the rare ability to take complex topics and explain them clearly, as shown by the success of her ten previous books on Access. Balter is known for providing real-world solutions to specific Access development problems. She also is known for her ability to back up her practical examples with just enough underlying theory to give the reader a good overall understanding of Access. In short, this book will provide beginning and intermediate Access developers with everything that they need to know to design and build Access 2007 applications. It should also appeal to DBAs and power users who want or need to get started building custom Access apps. This latest book in her Mastering Access series will not disappoint her many fans who anxiously await each new version, and should win her new fans as well.

A Guide to NIP Theories

A Guide to NIP Theories
Author: Pierre Simon
Publisher: Cambridge University Press
Total Pages: 165
Release: 2015-07-16
Genre: Mathematics
ISBN: 1107057752

The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.

Encyclopaedia of Mathematics

Encyclopaedia of Mathematics
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
Total Pages: 595
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401512884

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Handbook of Mathematics

Handbook of Mathematics
Author: Thierry Vialar
Publisher: BoD - Books on Demand
Total Pages: 1134
Release: 2016-12-07
Genre: Mathematics
ISBN: 2955199001

The book consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII .Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

Introductory Notes on Valuation Rings and Function Fields in One Variable

Introductory Notes on Valuation Rings and Function Fields in One Variable
Author: Renata Scognamillo
Publisher: Springer
Total Pages: 125
Release: 2014-07-01
Genre: Mathematics
ISBN: 8876425012

The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links with arithmetic are also often indicated. There are three appendices, concerning Hilbert’s Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompanied by hints, which sometimes develop further results not included in full for brevity reasons.