Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.
Positive Polynomials
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Editorial Reviews
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From the reviews of the first edition:
"This is a nicely written introduction to ‘reality’ and ‘positivity’ in rings, and besides students and researchers it can also be interesting for anyone who would like to learn more on positivity and orderings." (Vilmos Totik, Acta Scientiarum Mathematicarum, Vol. 68, 2002)
"A book on ‘real algebra’ that serves as an introduction to the subject in addition to the main theme of the text. … Well written with exercises for every chapter." (ASLIB Book Guide, Vol. 66 (11), 2001)
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Inside This Book
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First Sentence:
The most basic notion of real algebra and real analysis, in contrast to ordinary algebra and complex analysis, is the notion of "positivity." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
semialgebraic definition, prenex definition, convex valuation ring, real residue field, quadratic module, constructible topology, regular quadratic form, weak isotropy, spectral topology, convex subgroup, semialgebraic sets, real closure, interval topology, real closed field, positive cone, single indeterminate, distinguished representations, positive polynomials, residue map, unique ordering, real spectrum, valuation corresponding, total signature, valuation rings, finiteness theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tarski's Transfer, Local-Global Principle, Characterization Theorem, Finiteness Theorem, Schmüdgen's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The most basic notion of real algebra and real analysis, in contrast to ordinary algebra and complex analysis, is the notion of "positivity." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
semialgebraic definition, prenex definition, convex valuation ring, real residue field, quadratic module, constructible topology, regular quadratic form, weak isotropy, spectral topology, convex subgroup, semialgebraic sets, real closure, interval topology, real closed field, positive cone, single indeterminate, distinguished representations, positive polynomials, residue map, unique ordering, real spectrum, valuation corresponding, total signature, valuation rings, finiteness theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tarski's Transfer, Local-Global Principle, Characterization Theorem, Finiteness Theorem, Schmüdgen's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 35
books:
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- Model Theory (Encyclopedia of Mathematics and its Applications) by Wilfrid Hodges in Back Matter (1), and Back Matter (2)
- Model Theory, Third Edition (Studies in Logic and the Foundations of Mathematics) by C.C. Chang on page 40, and Back Matter
- Real Algebraic Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) by Jacek Bochnak in Back Matter (1), and Back Matter (2)
- Complex Semisimple Lie Algebras by Jean-Pierre Serre in Back Matter
- Foundations of Geometry by David Hilbert on page 28
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