Quadratic and Hermitian Forms

Released on by W. Scharlau
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  • Quadratic and Hermitian Forms Book Detail

  • Author : W. Scharlau
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 431
  • ISBN 13 : 3642699715
  • File Size : 1,1 MB
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Quadratic and Hermitian Forms by W. Scharlau PDF Summary

Book Description: 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.

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Quadratic and Hermitian Forms

Quadratic and Hermitian Forms

File Size : 52,52 MB
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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 theor

Quadratic and Hermitian Forms

Quadratic and Hermitian Forms

File Size : 16,16 MB
Total View : 9900 Views
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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 over Rings

Quadratic and Hermitian Forms over Rings

File Size : 79,79 MB
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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 i

Quadratic and Hermitian Forms Over Rings

Quadratic and Hermitian Forms Over Rings

File Size : 23,23 MB
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This book presents the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the chara