%0 Journal Article
%A Gamboa Mutuberria, José Manuel
%T On Prime Ideals In Rings Of Semialgebraic Functions
%D 1993
%@ 0002-9939
%U https://hdl.handle.net/20.500.14352/57279
%X It 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.
%~