|
Orderings and maximal ideals of rings of analytic functions
Author(s):
A.
Díaz-Cano
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2821-2828.
MSC (2000):
Primary 14P15, 32B15, 32B20
Posted:
March 24, 2005
MathSciNet review:
2159758
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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  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  is compact. This approach is also useful for studying the orderings of the field of meromorphic functions on  .
References:
-
- [AB90]
- 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. MR 1051200 (92c:14055) - [ABR96]
- C. Andradas, L. Bröcker, J. M. Ruiz.
Constructible sets in real geometry.
Springer-Verlag, Berlin, 1996. MR 1393194 (98e:14056) - [BCR98]
- J. Bochnak, M. Coste, M.-F. Roy.
Real Algebraic Geometry.
Springer-Verlag, Berlin, 1998. MR 1659509 (2000a:14067) - [Cas91]
- A. Castilla.
Sums of 2 -th powers of meromorphic functions with compact zero set.
Lect. Notes Math. 1524 (1991), 174-177. MR 1226251 (94e:32016) - [Cas94a]
- A. Castilla.
Artin-Lang property for analytic manifolds of dimension two.
Math. Z. 217 (1994), 5-14.MR 1292169 (95g:32011) - [Cas94b]
- A. Castilla.
Propiedad de Artin-Lang para variedades analíticas de dimensión dos.
Ph. D. Thesis, Universidad Complutense de Madrid (1994). - [DA01]
- A. Díaz-Cano, C. Andradas.
Complexity of global semianalytic sets in a real analytic manifold of dimension 2.
J. reine angew. Math. 534 (2001), 195-208. MR 1831638 (2002b:32015) - [GJ60]
- L. Gillman, M. Jerison.
Rings of continuous functions.
Van Nostrand, Princeton, 1960. MR 0116199 (22:6994) - [Hir76]
- M. Hirsch.
Differential Topology.
Springer-Verlag, 1976. MR 0448362 (56:6669) - [Jaw91]
- P. Jaworski.
The 17-th Hilbert problem for noncompact real analytic manifolds.
Lecture Notes Math. 1524 (1991), 289-295. MR 1226260 (95b:14040) - [KR89]
- K. Kurdyka, G. Raby.
Densité des ensembles sous-analytiques.
Ann. Inst. Fourier 39 (1989), 753-771. MR 1030848 (90k:32026)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
14P15, 32B15, 32B20
Retrieve articles in all Journals with
MSC (2000):
14P15, 32B15, 32B20
Additional Information:
A.
Díaz-Cano
Affiliation:
Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email:
Antonio_DiazCano@mat.ucm.es
DOI:
10.1090/S0002-9939-05-07848-2
PII:
S 0002-9939(05)07848-2
Keywords:
Real analytic sets,
analytic functions,
maximal ideals,
ultrafilters,
orderings
Received by editor(s):
November 20, 2002
Received by editor(s) in revised form:
May 20, 2004
Posted:
March 24, 2005
Additional Notes:
This work was supported by the European Community's Human Potential Programme under contract HPRN-CT-2001-00271, RAAG and by the Spanish Research Project GAAR BFM2002-04797.
Dedicated:
Dedicated to Eberhard Becker on the occasion of his 60th birthday
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
