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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Quadratic and Hermitian Forms

Quadratic and Hermitian Forms

Scharlau, W.

Paperback

Series: Grundlehren Der Mathematischen Wissenschaften, Book 270

AlgebraGeneral Mathematics

ISBN10: 3642699731
ISBN13: 9783642699733
Publisher: Springer Nature
Published: Dec 10 2011
Pages: 422
Weight: 1.34
Height: 0.89 Width: 6.14 Depth: 9.21
Language: English
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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