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Squares

Squares

£39.99

Part of London Mathematical Society Lecture Note Series

  • Date Published: October 1993
  • availability: Available
  • format: Paperback
  • isbn: 9780521426688

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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 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.

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    Product details

    • Date Published: October 1993
    • format: Paperback
    • isbn: 9780521426688
    • length: 300 pages
    • dimensions: 229 x 152 x 17 mm
    • weight: 0.44kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    A. R. Rajwade, Panjab University, Japan

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