Publication: On Prime Ideals In Rings Of Semialgebraic Functions
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Publication Date
1993
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American Mathematical Society
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Abstract
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.
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