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Author : R. Baeza
Publisher : Springer
ISBN 13 : 3540358161
Total Pages : 204 pages
Book Rating : 4.69/5 ( download)
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:
Author : Ricardo Baeza
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.07/5 ( download)
Download or read book Quadratic forms over semilocal rings written by Ricardo Baeza and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kenneth I. Mandelberg
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.29/5 ( download)
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:
Author : Roger David Peterson
Publisher :
ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.31/5 ( download)
Download or read book A Group Ring Invariant for Finite Groups and Quadratic Forms Over Semi-local Rings written by Roger David Peterson and published by . This book was released on 1973 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Max-Albert Knus
Publisher : Springer Science & Business Media
ISBN 13 : 3642754015
Total Pages : 536 pages
Book Rating : 4.12/5 ( download)
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.
Author : K. Zainoulline
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.08/5 ( download)
Download or read book On Knebusch's Norm Principle for Quadratic Forms Over Semi-local Rings written by K. Zainoulline and published by . This book was released on 2003 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. Scharlau
Publisher : Springer Science & Business Media
ISBN 13 : 3642699715
Total Pages : 431 pages
Book Rating : 4.19/5 ( download)
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.
Author : Tsit-Yuen Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821810952
Total Pages : 577 pages
Book Rating : 4.58/5 ( download)
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.
Author : Frank DeMeyer
Publisher : American Mathematical Soc.
ISBN 13 : 0821824570
Total Pages : 73 pages
Book Rating : 4.73/5 ( download)
Download or read book Quadratic Forms Over Q and Galois Extensions of Commutative Rings written by Frank DeMeyer and published by American Mathematical Soc.. This book was released on 1989 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of the first two sections of this memoir is to give explicit descriptions of both the Witt ring of the rational numbers [bold]Q and the set of abelian extensions of [bold]Q. The third presents a discussion around a particular case of the Galois cubic extension, building on the general theory.
Author : McMaster University
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860083
Total Pages : 362 pages
Book Rating : 4.89/5 ( download)
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).
