Gamboa Mutuberria, José Manuel2023-06-202023-06-2019930002-993910.2307/2160055https://hdl.handle.net/20.500.14352/57279It is proved that if p is a prime ideal in the ring S{M) of semialgebraic functions on a semialgebraic set M, the quotient field of S(M)/p is real closed. We also prove that in the case where M is locally closed, the rings S(M) and P(M)—polynomial functions on M—have the same Krull dimension. The proofs do not use the theory of real spectra.engjournal articlehttp://www.ams.org/journals/proc/1993-118-04/S0002-9939-1993-1140669-6/S0002-9939-1993-1140669-6.pdfhttp://www.ams.orgrestricted access512.7Prime Ideal In The Ring Of Semialgebraic FunctionsKrull DimensionGeometria algebraica1201.01 Geometría Algebraica