Buch, Englisch, 268 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 429 g
From Hilbert's 17th Problem to Real Algebra
Buch, Englisch, 268 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 429 g
Reihe: Springer Monographs in Mathematics
ISBN: 978-3-642-07445-5
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.
