Squares

Häftad, Engelska, 1993

Del 171 i serien London Mathematical Society Lecture Note Series

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Beskrivning

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 easily accessible to non-experts and undergraduates alike. The author deals with many different approaches to the study of squares; from the classical works of the late 19th century, to areas of current research. Anyone with an interest in algebra or number theory will find this a most fascinating volume.

Produktinformation

Utgivningsdatum:1993-10-14
Mått:151 x 228 x 20 mm
Vikt:393 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Lecture Note Series
Antal sidor:300
Förlag:Cambridge University Press
ISBN:9780521426688

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Recensioner i media

"A well-written, unpretentious introduction to squares and sums of squares in fields." American Mathematical Monthly

Innehållsförteckning

1. The theorem of Hurwitz; 2. The 2n theorems and the Stufe of fields; 3. Examples of the Stufe of fields and related topics; 4. Hilbert's 17th problem; 5. Positive definite functions and sums of squares; 6. An introduction to Hilbert's theorem; 7. The two proofs of Hilbert's theorem; 8. Theorems of Reznick and Choi, Lam and Reznick; 9. Theorems of Choi, Calderon and Robinson; 10. The theorem of Hurwitz–Radon; 11. An introduction to quadratic form theory; 12. The theory of multiplicative forms and Pfister forms; 13. The Hopf condition; 14. Examples of bilinear identities and a theorem of Gabel; 15. Artin–Schreier theory of formally real fields; 16. Squares and sums of squares in fields and their extension fields; 17. Pourchet's theorem and related results; 18. Examples of the Stufe and Pythagoras number of fields using the Hasse–Minkowski theorem; Appendix: Reduction of matrices to canonical form.