On connectedness of sets in the real spectra of polynomial rings

DOI10.1007/s00229-008-0244-1zbMath1169.14039arXivmath/0601671OpenAlexW2075540505MaRDI QIDQ1014805

James J. Madden, Mark Spivakovsky, François Lucas, Daniel Schaub

Publication date: 29 April 2009

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601671

zbMATH Keywords

real spectrumpolynomial ringblowing-upreal closed fieldpiecewise polynomial functions

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Real algebra (13J30)

Related Items (7)

On points at infinity of real spectra of polynomial rings ⋮ Approximate roots of a valuation and the Pierce-Birkhoff conjecture ⋮ Henriksen and Isbell on \(f\)-rings ⋮ On the Pierce-Birkhoff conjecture for smooth affine surfaces over real closed fields ⋮ On the Pierce-Birkhoff conjecture ⋮ Discrete piecewise linear functions ⋮ On the strong separation conjecture

Cites Work

• Approximate roots of a valuation and the Pierce-Birkhoff conjecture
• Pierce-Birkhoff rings
• On the Pierce-Birkhoff conjecture over ordered fields
• Lectures on formally real fields
• On the Pierce-Birkhoff conjecture in three variables
• Lattice ordered rings and function rings
• Maximal fields with valuations
• The Pierce-Birkhoff Conjecture for Curves
• Allgemeine Bewertungstheorie.
• On the Pierce-Birkhoff conjecture
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