000			03102nam a22003618i 4500
001			CR9780511566028
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090518s1993||||enk o ||1 0|eng|d
020			_a9780511566028 (ebook)
020			_z9780521426688 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA243 _b.R35 1993
082	0	0	_a512/.74 _220
100	1		_aRajwade, A. R., _eauthor.
245	1	0	_aSquares / _cA.R. Rajwade.
264		1	_aCambridge : _bCambridge University Press, _c1993.
300			_a1 online resource (xii, 286 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v171
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aThe 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).
520			_aMany 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.
650		0	_aForms, Quadratic.
650		0	_aSequences (Mathematics)
776	0	8	_iPrint version: _z9780521426688
830		0	_aLondon Mathematical Society lecture note series ; _v171.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511566028
999			_c517808 _d517806