Springer Monographs in Mathematics: From Hilbert’s 17th Problem to Real Algebra

Prestel, Alexander; Delzell, Charles

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.

Details

Published by: Springer

Publication Date: 2001-04-24

Format: Hardcover

ISBN-13: 9783540412151

DOI: 10.1007/978-3-662-04648-7

Dimensions: 235cm x155cm

Pages: 268