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Orderings and maximal ideals of rings of analytic functions.

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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


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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
Deposited On:27 Apr 2012 09:05
Last Modified:20 Apr 2015 11:55

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