Baro González, ElíasFernando Galván, José FranciscoGamboa Mutuberria, José Manuel2025-05-162025-05-162025https://hdl.handle.net/20.500.14352/120132We 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.engjournal articleopen accessAlgebraic geometryGeometria algebraica1201.01 Geometría Algebraica