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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Official URL: http://www.ams.org/journals/proc/2005-133-10/S0002-9939-05-07848-2/S0002-9939-05-07848-2.pdf

## 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 |
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Uncontrolled Keywords: | Real analytic sets; Analytic functions; Maximal ideal; Ultrafilters; orderings. |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15040 |

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Deposited On: | 27 Apr 2012 09:05 |

Last Modified: | 06 Feb 2014 10:14 |

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