Real Algebraic and Analytic Geometry |

Orderings and maximal ideals of rings of analytic functions.

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Submission: 2002, December 18.

*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 to study the orderings of the field of meromorphic
functions on $X$.*

Mathematics Subject Classification (2000): 14P15, 32B15, 32B20.

Keywords and Phrases: Real analytic sets, analytic functions, maximal ideals, ultrafilters, orderings.

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