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Orderings and maximal ideals of rings of analytic functions.

Díaz-Cano Ocaña, Antonio (2005) Orderings and maximal ideals of rings of analytic functions. Proceedings of the American Mathematical Society, 133 (10). pp. 2821-2828. ISSN 1088-6826

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Abstract

We prove that there is a natural injective correspondence between the maximal ideals of the ring of analytic functions on a real analytic set X and those of its subring of bounded analytic functions. By describing the maximal ideals in terms of ultrafilters we see that this correspondence is surjective if and only if X is compact. This approach is also useful for studying the orderings of the field of meromorphic functions on X.

Item Type:Article
Uncontrolled Keywords:Real analytic sets; Analytic functions; Maximal ideal; Ultrafilters; orderings.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15040
References:

C. Andradas, E. Becker. A note on the real spectrum of analytic functions on an analytic manifold of dimension one. Lect. Notes Math. 1420 (1990), 1–21.

C. Andradas, L. Br¨ocker, J. M. Ruiz. Constructible sets in real geometry. Springer- Verlag, Berlin, 1996.

J. Bochnak, M. Coste, M.-F. Roy. Real Algebraic Geometry. Springer-Verlag, Berlin, 1998.

A. Castilla. Sums of 2n-th powers of meromorphic functions with compact zero set. Lect. Notes Math. 1524 (1991), 174–177.

A. Castilla. Artin-Lang property for analytic manifolds of dimension two. Math. Z. 217 (1994), 5–14.

A. Castilla. Propiedad de Artin-Lang para variedades anal´ıticas de dimensi´on dos. Ph. D. Thesis, Universidad Complutense de Madrid (1994).

A. D´ıaz-Cano, C. Andradas. Complexity of global semianalytic sets in a real analytic manifold of dimension 2. J. reine angew. Math. 534 (2001), 195–208.

L. Gillman, M. Jerison. Rings of continuous functions. Van Nostrand, Princeton, 1960.

M. Hirsch. Differential Topology. Springer-Verlag, 1976.

P. Jaworski. The 17-th Hilbert problem for noncompact real analytic manifolds. Lecture Notes Math. 1524 (1991), 289–295.

K. Kurdyka, G. Raby. Densit´e des ensembles sous-analytiques. Ann. Inst. Fourier 39(1989), 753–771.

Deposited On:27 Apr 2012 09:05
Last Modified:06 Feb 2014 10:14

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