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Real Algebra

  • Carlos Andradas
  • Ludwig Bröcker
  • Jesús M. Ruiz
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge A Series of Modern Surveys in Mathematics book series (MATHE3, volume 33)

Summary

We consider general properties of the real spectrum of a commutative ring with unit. In Sections 1 and 2 we collect the basic facts, and for more information we refer to [B-C-R] and [Kn-Schd]. In Section 3 valuation theory enters the scene. It is of fundamental importance for the whole work. As an application we obtain in Section 4 the first results on going-up and going-down in the real spectrum. In Section 5 we present the notion and basic properties of abstract semialgebraic functions on constructible sets of the real spectrum; this is done in two equivalent ways which have both their advantages. These functions are used in Section 6 to construct cylindrical decompositions with respect to systems of polynomials. Finally, in Section 7 we introduce real strict localizations, which are the real analogues of the strict localizations used in etale cohomology.

Keywords

Local Ring Commutative Ring Valuation Ring Residue Field Real Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Carlos Andradas
    • 1
  • Ludwig Bröcker
    • 2
  • Jesús M. Ruiz
    • 3
  1. 1.Departamento de AlgebraUniversidad Complutense de MadridMadridSpain
  2. 2.Mathematisches InstitutUniversität MünsterMünsterGermany
  3. 3.Departamento de Geometría y TopologíaUniversidad Complutense de MadridMadridSpain

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