RT Journal Article
T1 Intermediate algebras of semialgebraic functions
A1 Baro González, Elías
A1 Fernando Galván, José Francisco
A1 Gamboa Mutuberria, José Manuel
AB 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.
YR 2025
FD 2025
LK https://hdl.handle.net/20.500.14352/120132
UL https://hdl.handle.net/20.500.14352/120132
LA eng
DS Docta Complutense
RD 8 jun 2025