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Catalogue Information
Field name	Details
Dewey Class	512
Title	Positive Polynomials ([EBook]) : From Hilbert’s 17th Problem to Real Algebra / by Alexander Prestel, Charles N. Delzell.
Author	Prestel, Alexander
Added Personal Name	Delzell, Charles N.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2001.
Physical Details	VIII, 269 pages : online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9783662046487
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-04648-7
Links to Related Works	Subject References: Algebra . Algebraic Geometry . Functional Analysis . Mathematics . Polynomials . Authors: author . Delzell, Charles N. . Prestel, Alexander . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 512 .

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Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra

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