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Quadratic and Hermitian Forms (Paperback, Softcover reprint of the original 1st ed. 1985)
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Quadratic and Hermitian Forms (Paperback, Softcover reprint of the original 1st ed. 1985)
Series: Grundlehren der mathematischen Wissenschaften, 270
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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 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."
General
Imprint: |
Springer-Verlag
|
Country of origin: |
Germany |
Series: |
Grundlehren der mathematischen Wissenschaften, 270 |
Release date: |
December 2011 |
First published: |
1985 |
Authors: |
W. Scharlau
|
Dimensions: |
235 x 155 x 28mm (L x W x T) |
Format: |
Paperback
|
Pages: |
422 |
Edition: |
Softcover reprint of the original 1st ed. 1985 |
ISBN-13: |
978-3-642-69973-3 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Number theory >
General
|
LSN: |
3-642-69973-1 |
Barcode: |
9783642699733 |
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