On the Pierce-Birkhoff conjecture over ordered fields

DOI10.1216/RMJ-1989-19-3-651zbMath0715.14047OpenAlexW2006534418WikidataQ122860395 ScholiaQ122860395MaRDI QIDQ752124

Charles N. Delzell

Publication date: 1989

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-1989-19-3-651

zbMATH Keywords

piecewise polynomial functionpiecewise rational functionsPierce Birkhoff conjecture

Mathematics Subject Classification ID

Real algebraic sets (14P05) Semialgebraic sets and related spaces (14P10) Approximation by polynomials (41A10) Ordered rings, algebras, modules (06F25)

Related Items (12)

Extending piecewise polynomial functions in two variables ⋮ Virtual roots of real polynomials ⋮ Approximate roots of a valuation and the Pierce-Birkhoff conjecture ⋮ Extension of the two-variable Pierce-Birkhoff conjecture to generalized polynomials ⋮ Free bounded Archimedean \(\ell\)-algebras ⋮ On the Pierce-Birkhoff conjecture ⋮ A canonical form for the continuous piecewise polynomial functions ⋮ Pierce-Birkhoff rings ⋮ On the Pierce-Birkhoff conjecture in three variables ⋮ On connectedness of sets in the real spectra of polynomial rings ⋮ On the strong separation conjecture ⋮ A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field

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