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On Prime Ideals In Rings Of Semialgebraic Functions


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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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

J. Bochnak, M. Coste, and M. F. Roy, Geometric algebrique reelle, Ergeb. Math. Grenzgeb.(3), vol. 12, Springer-Verlag, Berlin and New York, 1987.

M. Carral and M. Coste, Normal spectral spaces and their dimensions, J. Pure Appl. Algebra 301 (1983), 227-235.

3. J. M. Gamboa and J. M. Ruiz, On rings of semialgebraic functions, Math. Z. 206 (1991), 527-532.

M. Henriksen and J. R. Isbell, On the continuity of the real roots of an algebraic equation, Proc. Amer. Math. Soc. 4 (1953), 431-434.

J. R. Isbell, More on the continuity of the real roots of an algebraic equation, Proc. Amer. Math. Soc. 5(1954), 439.

T. Recio, Una descomposicion de un conjunlo semialgebraico, Proc. A.M.E.L. Mallorca, 1977.

J. J. Risler, Le theoreme des zeros en geometries algebrique et analytique relies, Bull. Soc. Math. France 104 (1976), 113-127.

J. M. Ruiz, Cones locaux et completions, C.R. Acad. Sci. Paris Ser. I Math. 302 (1986), 67-69.

N. Schwartz, The basic theory of real closed spaces, Mem. Amer. Math. Soc, no. 397, Amer. Math. Soc, Providence, RI, 1989.

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Last Modified:02 Mar 2016 14:27

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