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Algebraic Theory Of Quadratic Forms

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The Algebraic Theory Of Quadratic Forms

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Author : Tsit-Yuen Lam
language : en
Publisher:
Release Date : 1973

The Algebraic Theory Of Quadratic Forms written by Tsit-Yuen Lam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algebraic fields categories.

Algebraic Theory Of Quadratic Numbers

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Author : Mak Trifković
language : en
Publisher: Springer
Release Date : 2013-09-14

Algebraic Theory Of Quadratic Numbers written by Mak Trifković and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-14 with Mathematics categories.

By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory.

Bilinear Algebra

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Author : Kazimierz Szymiczek
language : en
Publisher: CRC Press
Release Date : 1997-09-05

Bilinear Algebra written by Kazimierz Szymiczek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-05 with Mathematics categories.

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.

The Algebraic And Geometric Theory Of Quadratic Forms

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Author : Richard S. Elman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-07-15

The Algebraic And Geometric Theory Of Quadratic Forms written by Richard S. Elman 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 2008-07-15 with Mathematics categories.

This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

Algebraic Theory Of Quadratic Forms

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Author : Manfred Knebusch
language : en
Publisher: Birkhäuser
Release Date : 1980

Algebraic Theory Of Quadratic Forms written by Manfred Knebusch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Juvenile Nonfiction categories.

Introduction To Quadratic Forms

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Author : Onorato Timothy O’Meara
language : en
Publisher: Springer
Release Date : 2013-12-01

Introduction To Quadratic Forms written by Onorato Timothy O’Meara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

Introduction To Quadratic Forms Over Fields

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Author : T.Y. Lam
language : en
Publisher: American Mathematical Soc.
Release Date :

Introduction To Quadratic Forms Over Fields written by T.Y. Lam 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 with Mathematics categories.

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.

Quadratic And Hermitian Forms

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

Quadratic And Hermitian Forms written by W. Scharlau 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 Mathematics categories.

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.

Bilinear Algebra

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Author : Kazimierz Szymiczek
language : en
Publisher: Routledge
Release Date : 2017-11-22

Bilinear Algebra written by Kazimierz Szymiczek and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

Algebraic Theory Of Quadratic Forms

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