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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1140669
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Abstract: It is proved that if $ \mathfrak{p}$ is a prime ideal in the ring $ S(M)$ of semialgebraic functions on a semialgebraic set $ M$, the quotient field of $ S(M)/\mathfrak{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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1140669-6
PII: S 0002-9939(1993)1140669-6
Article copyright: © Copyright 1993 American Mathematical Society