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＜電子ブック＞
Positive Polynomials : From Hilbert’s 17th Problem to Real Algebra / by Alexander Prestel, Charles Delzell
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2001.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2001
本文言語	英語
大きさ	VIII, 268 p : online resource
著者標目	*Prestel, Alexander author Delzell, Charles author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic geometry LCSH:Functional analysis FREE:Algebra FREE:Algebraic Geometry FREE:Functional Analysis
一般注記	1. Real Fields -- 2. Semialgebraic Sets -- 3. Quadratic Forms over Real Fields -- 4. Real Rings -- 5. Archimedean Rings -- 6. Positive Polynomials on Semialgebraic Sets -- 7. Sums of 2mth Powers -- 8. Bounds -- Appendix: Valued Fields -- A.1 Valuations -- A.2 Algebraic Extensions -- A.3 Henselian Fields -- A.4 Complete Fields -- A.5 Dependence and Composition of Valuations -- A.6 Transcendental Extensions -- A.7 Exercises -- A.8 Bibliographical Comments -- References -- Glossary of Notations Positivity is one of the most basic mathematical concepts. In many areas of mathematics (like analysis, real algebraic geometry, functional analysis, etc.) it shows up as positivity of a polynomial on a certain subset of R^n which itself is often given by polynomial inequalities. The main objective of the book is to give useful characterizations of such polynomials. It takes as starting point Hilbert's 17th Problem from 1900 and explains how E. Artin's solution of that problem eventually led to the development of real algebra towards the end of the 20th century. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed. Thus the monograph can also serve as the basis for a 2-semester course in real algebra HTTP:URL=https://doi.org/10.1007/978-3-662-04648-7

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