%0 Journal Article
%A Baro González, Elías
%A Fernando Galván, José Francisco
%A Gamboa Mutuberria, José Manuel
%T Intermediate algebras of semialgebraic functions
%D 2025
%U https://hdl.handle.net/20.500.14352/120132
%X We characterize intermediate ℝ-algebras A between the ring of semialgebraic functions (X) and the ring ∗(X) of bounded semialgebraic functions on a semialgebraic set X as rings of fractions of (X). This allows us to compute the Krull dimension of A, the transcendence degree over ℝ of the residue fields of A and to obtain a Łojasiewicz inequality and a Nullstellensatz for archimedean ℝ-algebras A. In addition we study intermediate ℝ-algebras generated by proper ideals and we prove an extension theorem for functions in such ℝ-algebras.
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