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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
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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  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  .
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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.
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