Download or read book Lectures on Formally Real Fields written by A. Prestel and published by Springer. This book was released on 2007-01-05 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Absolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization. In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.
Download or read book Analyse Complexe written by Alexander Prestel and published by . This book was released on 1984 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures in Abstract Algebra written by N. Jacobson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are of interest in number theory. A second objective of our ac count has been to indicate the links between the present theory of fields and the classical problems which led to its development.
Download or read book Lectures in Abstract Algebra Theory of fields and galois theory written by Nathan Jacobson and published by . This book was released on 1964 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Formally p adic Fields written by A. Prestel and published by Springer. This book was released on 2006-11-14 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Formal and Rigid Geometry written by Siegfried Bosch and published by Springer. This book was released on 2014-08-22 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Download or read book Groups Modules and Model Theory Surveys and Recent Developments written by Manfred Droste and published by Springer. This book was released on 2017-06-02 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Download or read book Lectures in Abstract Algebra Introduction written by Nathan Jacobson and published by . This book was released on 1951 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume Lectures are based on Jacobson's graduate lectures on algebra at Johns Hopkins and Yale in the 1940's and early 1950's, and are very careful, comprehensive and classical in style, giving a general treatment of abstract algebra. The first volume gives a comprehensive introduction to abstract algebra and its basic concepts. The second volume deals with the theory of vector spaces, accompanied by examples and exercises. The third and final volume addresses field theory and Galois theory, and is not an easy read for the casual student, but a serious student who works at the material will be repaid for their efforts. All volumes include a considerable number of exercises are given that vary greatly in difficulty, while the texts in general are example-driven and user-friendly.
Download or read book The Absolute Galois Group of a Semi Local Field written by Dan Haran and published by Springer Nature. This book was released on 2021-11-19 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.
Download or read book Spectral Spaces written by Max Dickmann and published by Cambridge University Press. This book was released on 2019-03-21 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.
Download or read book Geometrie algebrique reelle et formes quadratiques written by J.-L. Colliot-Thelene and published by Springer. This book was released on 2006-11-15 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quadratic and Hermitian Forms written by McMaster University and published by American Mathematical Soc.. This book was released on 1984 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).
Download or read book Ten Lectures on Quadratic Forms Over Fields written by G. Orzech and published by . This book was released on 1977 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Shorter Model Theory written by Wilfrid Hodges and published by Cambridge University Press. This book was released on 1997-04-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by Routledge. This book was released on 2017-11-22 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.
Download or read book K Theory and Algebraic Geometry Connections with Quadratic Forms and Division Algebras written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1995 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of two - also available in a set of both volumes.
Download or read book From Dedekind to G del written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
