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Squares /
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 |
MARC
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| 100 | 1 | |a Rajwade, A. R. | |
| 245 | 1 | 0 | |a Squares / |c A.R. Rajwade. |
| 260 | |a Cambridge ; |a New York, NY, USA : |b Cambridge University Press, |c 1993. | ||
| 300 | |a 1 online resource (xii, 286 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 171 | |
| 504 | |a Includes bibliographical references (pages 279-284) and index. | ||
| 505 | 0 | |a 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). | |
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Forms, Quadratic. | |
| 650 | 0 | |a Sequences (Mathematics) | |
| 650 | 6 | |a Formes quadratiques. | |
| 650 | 6 | |a Suites (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 650 | 7 | |a Forms, Quadratic |2 fast | |
| 650 | 7 | |a Sequences (Mathematics) |2 fast | |
| 650 | 7 | |a Quadratische Form |2 gnd | |
| 650 | 1 | 7 | |a Kwadratische systemen. |2 gtt |
| 650 | 7 | |a Formes quadratiques. |2 ram | |
| 776 | 0 | 8 | |i Print version: |a Rajwade, A.R. |t Squares. |d Cambridge ; New York, NY, USA : Cambridge University Press, 1993 |z 0521426685 |w (DLC) 93167566 |w (OCoLC)29847819 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 171. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552440 |z Texto completo |
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