Quadratic And Hermitian Forms Over Rings

Download Quadratic And Hermitian Forms Over Rings full books in PDF, epub, and Kindle. Read online Quadratic And Hermitian Forms Over Rings ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Quadratic and Hermitian Forms over Rings

Author : Max-Albert Knus
Publisher : Springer Science & Business Media
ISBN 13 : 3642754015
Total Pages : 536 pages
Book Rating : 4.6/5 (427 download)

DOWNLOAD NOW!

Book Synopsis Quadratic and Hermitian Forms over Rings by : Max-Albert Knus

Download or read book Quadratic and Hermitian Forms over Rings written by Max-Albert Knus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.

Quadratic and Hermitian Forms

Author : McMaster University
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860083
Total Pages : 362 pages
Book Rating : 4.8/5 (6 download)

DOWNLOAD NOW!

Book Synopsis Quadratic and Hermitian Forms by : McMaster University

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).

Quadratic and Hermitian Forms

Author : W. Scharlau
Publisher : Springer Science & Business Media
ISBN 13 : 3642699715
Total Pages : 431 pages
Book Rating : 4.6/5 (426 download)

DOWNLOAD NOW!

Book Synopsis Quadratic and Hermitian Forms by : W. Scharlau

Download or read book Quadratic and Hermitian Forms written by W. Scharlau and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms. On the basis of their work, Minkowski, Siegel, Hasse, Eichler and many others crea ted the impressive "arithmetic" theory of quadratic forms, which has been the object of the well-known books by Bachmann (1898/1923), Eichler (1952), and O'Meara (1963). Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both - the number theory of quadratic forms and the ideas of modern algebra - Witt opened, in 1937, a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object. This object - the Witt ring - then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems.

Introduction to Quadratic Forms over Fields

Author : Tsit-Yuen Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821810952
Total Pages : 577 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Quadratic Forms over Fields by : Tsit-Yuen Lam

Download or read book Introduction to Quadratic Forms over Fields written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 2005 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.

Faithfully Quadratic Rings

Author : M. Dickmann
Publisher : American Mathematical Soc.
ISBN 13 : 1470414686
Total Pages : 129 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Faithfully Quadratic Rings by : M. Dickmann

Download or read book Faithfully Quadratic Rings written by M. Dickmann and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.

Handbook of Algebra

Author : M. Hazewinkel
Publisher : Elsevier
ISBN 13 : 9780080932811
Total Pages : 592 pages
Book Rating : 4.9/5 (328 download)

DOWNLOAD NOW!

Book Synopsis Handbook of Algebra by : M. Hazewinkel

Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2009-07-08 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

The Algebraic Theory of Quadratic Forms

Author : Tsit-Yuen Lam
Publisher : Addison-Wesley
ISBN 13 : 9780805356663
Total Pages : 344 pages
Book Rating : 4.3/5 (566 download)

DOWNLOAD NOW!

Book Synopsis The Algebraic Theory of Quadratic Forms by : Tsit-Yuen Lam

Download or read book The Algebraic Theory of Quadratic Forms written by Tsit-Yuen Lam and published by Addison-Wesley. This book was released on 1980 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ordered Algebraic Structures and Related Topics

Author : Fabrizio Broglia
Publisher : American Mathematical Soc.
ISBN 13 : 1470429667
Total Pages : 366 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Ordered Algebraic Structures and Related Topics by : Fabrizio Broglia

Download or read book Ordered Algebraic Structures and Related Topics written by Fabrizio Broglia and published by American Mathematical Soc.. This book was released on 2017 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the international conference ""Ordered Algebraic Structures and Related Topics'', held from October 12-16, 2015, at CIRM, Luminy, Marseilles, France. Papers contained in this volume cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.

Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups

Author : Carl R. Riehm
Publisher : American Mathematical Soc.
ISBN 13 : 0821885952
Total Pages : 305 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups by : Carl R. Riehm

Download or read book Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups written by Carl R. Riehm and published by American Mathematical Soc.. This book was released on with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Advances in Real Algebraic Geometry and Quadratic Forms

Author : Bill Jacob
Publisher : American Mathematical Soc.
ISBN 13 : 0821851543
Total Pages : 405 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Recent Advances in Real Algebraic Geometry and Quadratic Forms by : Bill Jacob

Download or read book Recent Advances in Real Algebraic Geometry and Quadratic Forms written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1994 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume grew out of a year-long program in ``Real Algebraic Geometry and Quadratic Forms'', held at the University of California at Berkeley during the 1990-1991 academic year. This valuable collection of research articles by top workers serves as a record of current developments in these areas and as a tribute to the fruitful interaction between them. Students and researchers alike will find this book a useful reference, with articles ranging from the technical to the expository. Also included are summaries of the current developments in several sub-disciplines and indications of new research directions.

Quadratic Forms Over Semilocal Rings

Author : R. Baeza
Publisher : Springer
ISBN 13 : 3540358161
Total Pages : 204 pages
Book Rating : 4.5/5 (43 download)

DOWNLOAD NOW!

Book Synopsis Quadratic Forms Over Semilocal Rings by : R. Baeza

Download or read book Quadratic Forms Over Semilocal Rings written by R. Baeza and published by Springer. This book was released on 2006-11-22 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quadratic Forms Over Semi-local Rings

Author : Kenneth I. Mandelberg
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.E/5 ( download)

DOWNLOAD NOW!

Book Synopsis Quadratic Forms Over Semi-local Rings by : Kenneth I. Mandelberg

Download or read book Quadratic Forms Over Semi-local Rings written by Kenneth I. Mandelberg and published by . This book was released on 1973 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Symmetric Bilinear Forms

Author : John Milnor
Publisher : Springer Science & Business Media
ISBN 13 : 3642883303
Total Pages : 150 pages
Book Rating : 4.6/5 (428 download)

DOWNLOAD NOW!

Book Synopsis Symmetric Bilinear Forms by : John Milnor

Download or read book Symmetric Bilinear Forms written by John Milnor and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts ...

Handbook of K-Theory

Author : Eric Friedlander
Publisher : Springer Science & Business Media
ISBN 13 : 354023019X
Total Pages : 1148 pages
Book Rating : 4.5/5 (42 download)

DOWNLOAD NOW!

Book Synopsis Handbook of K-Theory by : Eric Friedlander

Download or read book Handbook of K-Theory written by Eric Friedlander and published by Springer Science & Business Media. This book was released on 2005-07-18 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

Quadratic Forms and Their Applications

Author : Eva Bayer-Fluckiger
Publisher : American Mathematical Soc.
ISBN 13 : 0821827790
Total Pages : 311 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Quadratic Forms and Their Applications by : Eva Bayer-Fluckiger

Download or read book Quadratic Forms and Their Applications written by Eva Bayer-Fluckiger and published by American Mathematical Soc.. This book was released on 2000 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines the proceedings of the conference on 'Quadratic Forms and Their Applications' held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.

Computations with Modular Forms

Author : Gebhard Böckle
Publisher : Springer Science & Business Media
ISBN 13 : 3319038478
Total Pages : 376 pages
Book Rating : 4.3/5 (19 download)

DOWNLOAD NOW!

Book Synopsis Computations with Modular Forms by : Gebhard Böckle

Download or read book Computations with Modular Forms written by Gebhard Böckle and published by Springer Science & Business Media. This book was released on 2014-01-23 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.

Graded Rings and Graded Grothendieck Groups

Author : Roozbeh Hazrat
Publisher : Cambridge University Press
ISBN 13 : 1316619583
Total Pages : 244 pages
Book Rating : 4.3/5 (166 download)

DOWNLOAD NOW!

Book Synopsis Graded Rings and Graded Grothendieck Groups by : Roozbeh Hazrat

Download or read book Graded Rings and Graded Grothendieck Groups written by Roozbeh Hazrat and published by Cambridge University Press. This book was released on 2016-05-26 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.