Real Algebraic Geometry and Ordered Structures / Edition 1

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Brand new. We distribute directly for the publisher. This volume contains 16 carefully refereed articles by participants in the Special Session on Real Algebraic Geometry and ... Ordered Algebraic Structures at the Sectional Meeting of the AMS in Baton Rouge, April 1996, and the associated Special Semester in the spring of 1996 at Louisiana State University and Southern University, Baton Rouge. The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated.Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places.This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures--two subjects that are obviously related, but seldom brought together. Read more Show Less

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Overview

This volume contains 16 carefully refereed articles by participants in the Special Session on Real Algebraic Geometry and Ordered Algebraic Structures at the Sectional Meeting of the AMS in Baton Rouge, April 1996, and the associated Special Semester in the spring of 1996 at Louisiana State University and Southern University, Baton Rouge. The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures—two subjects that are obviously related, but seldom brought together.

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Editorial Reviews

Booknews
Contains 16 papers from an April 1996 meeting by 23 contributors, providing an overview of the field and encompassing both expository and original research. Topics include topology of real algebraic curves, effective sums of squares of real forms, efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, and radial vector fields. Other subjects are exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, and abstract spaces of higher-level orderings and real places. Lacks a subject index. Annotation c. Book News, Inc., Portland, OR booknews.com
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Product Details

  • ISBN-13: 9780821808047
  • Publisher: American Mathematical Society
  • Publication date: 3/1/2000
  • Series: Contemporary Mathematics Series , #253
  • Edition number: 1
  • Pages: 287

Table of Contents

Preface ix
On real involutions and ramifications of real valuations 1
Deciding positivity of real polynomials 19
Radial vector fields and the Poincare-Hopf theorem 25
A generalization of the Arnold-Viro inequalities for real singular algebraic curves 31
Floppy curves, with applications to real algebraic curves 39
Towards an abstract description of the space of real places 77
A special quantifier elimination algorithm for Pham systems 115
A look at biseparating maps from an algebraic point of view 135
Real Teichmuller spaces and moduli of real algebraic curves 145
Correction to "A real algebraic vector bundle is strongly algebraic whenever its total space is affine" 179
The exponential rank of nonarchimedean exponential fields 181
Subanalytic and semialgebraic realisations of abstract stratified sets 203
On the vector space defect for valued field extensions 209
On the classification of decomposable 7-th degree curves 219
The complex spectrum of a ring 235
Some concrete aspects of Hilbert's 17th problem 251
Semialgebraic singularity theory 273
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