On the Pierce-Birkhoff conjecture in three variables

DOI10.1016/j.jpaa.2007.01.012zbMath1130.13014OpenAlexW2018908534WikidataQ122947941 ScholiaQ122947941MaRDI QIDQ995607

Louis Mahé

Publication date: 3 September 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2007.01.012

zbMATH Keywords

semi-algebraic setsemi-algebraic functionpiecewise polynomialcylindrial decomposition

Mathematics Subject Classification ID

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

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Extending piecewise polynomial functions in two variables ⋮ Henriksen and Isbell on \(f\)-rings ⋮ On the Pierce-Birkhoff conjecture ⋮ On connectedness of sets in the real spectra of polynomial rings ⋮ On the strong separation conjecture

Cites Work

• Pierce-Birkhoff rings
• On the Pierce-Birkhoff conjecture over ordered fields
• Lattice ordered rings and function rings
• The Pierce-Birkhoff Conjecture for Curves
• Complete Ideals Defined by Sign Conditions and the Real Spectrum of a Two‐dimensional Local Ring
• On the Pierce-Birkhoff conjecture
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