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On Prime Ideals In Rings Of Semialgebraic Functions

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Gamboa, J. M. (1993) On Prime Ideals In Rings Of Semialgebraic Functions. Proceedings of the American Mathematical Society, 118 (4). pp. 1037-1041. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/1993-118-04/S0002-9939-1993-1140669-6/S0002-9939-1993-1140669-6.pdf


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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.


Item Type:Article
Uncontrolled Keywords:Prime Ideal In The Ring Of Semialgebraic Functions; Krull Dimension
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15368
Deposited On:25 May 2012 09:13
Last Modified:22 Aug 2018 10:09

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