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Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are ea...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York, NY, USA :
Cambridge University Press,
1993.
|
| Colección: | London Mathematical Society lecture note series ;
171. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- The theorem of Hurwitz (1898) on the 2, 4, 8-identities
- The 2n-identities and the Stufe of fields : theorems of Pfister and Cassels
- Examples of the Stufe of fields and related topics
- Hilbert's 17th problem and the function fields R(X), Q(X), and R(X, Y)
- Positive semi-definite functions and sums of squares in R(X1,X2 ..., Xn)
- Introduction to Hilbert's theorem (1888) in the ring R[X1,X2 ..., Xn]
- The two proofs of Hilbert's main theorem; Hilbert's own and the other of Choi and Lam
- Theorems of Reznick and of Choi, Lam and Reznick
- Theorems of Choi, Calderon and of Robinson
- The Radon function and the theorem of Hurwitz-Radon (1922-23)
- Introduction to the teory of quadratic forms
- Theory of multiplicative forms and of Pfister forms
- The rational admissibility of the triple (r, s, n) and the Hopf condition
- Some interesting examples of bilinear identities and a theorem of Gabel
- Artin-Schreier theory of formally real fields
- Squares and sums of squares in fields and their extension fields
- Pourchet's theorem that P(Q(X)) = 5 and related results
- Examples of the Stufe and pythagroas number of fields using the Hasse-Minkowski theorem
- Reduction of matrices to canonical forms (for Chapter 10)
- Convex sets (for chaptes 6,7,8,9).