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DíazCano Ocaña, Antonio (2005) Orderings and maximal ideals of rings of analytic functions. Proceedings of the American Mathematical Society, 133 (10). pp. 28212828. ISSN 10886826

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Official URL: http://www.ams.org/journals/proc/200513310/S0002993905078482/S0002993905078482.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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