On prime ideals in rings of semialgebraic functions
Author:
J. M. Gamboa
Journal:
Proc. Amer. Math. Soc. 118 (1993), 1037-1041
MSC:
Primary 14P10; Secondary 14P05
DOI:
https://doi.org/10.1090/S0002-9939-1993-1140669-6
MathSciNet review:
1140669
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Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that if is a prime ideal in the ring
of semialgebraic functions on a semialgebraic set
, the quotient field of
is real closed. We also prove that in the case where
is locally closed, the rings
and
--polynomial functions on
--have the same Krull dimension. The proofs do not use the theory of real spectra.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1993-1140669-6
Article copyright:
© Copyright 1993
American Mathematical Society