Publication: Orderings and maximal ideals of rings of analytic functions.
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Publication Date
2005
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America Mathematical Society
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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.
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