Orderings and maximal ideals of rings of analytic functions

Díaz-Cano, A.

doi:10.1090/S0002-9939-05-07848-2

Orderings and maximal ideals of rings of analytic functions
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Proc. Amer. Math. Soc. 133 (2005), 2821-2828 Request permission

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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