Grundlehren der mathematischen Wissenschaften

Quadratic and Hermitian Forms

Authors: Scharlau, W.

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About this book

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.

Table of contents (2 chapter)

  • Quadratic Forms over Fields

    Winfried Scharlau

    Pages 28-105

    Buy Chapter $29.95
  • Clifford Algebras

    Winfried Scharlau

    Pages 326-345

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Buy this book

eBook $99.00 net
( price for USA )
  • ISBN 978-3-642-69971-9
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $129.00 net
( price for USA )
  • ISBN 978-3-642-69973-3
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Quadratic and Hermitian Forms
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
270
Copyright
1985
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-69971-9
DOI
10.1007/978-3-642-69971-9
Softcover ISBN
978-3-642-69973-3
Series ISSN
0072-7830
Edition Number
1
Topics