%0 Journal Article
%A Díaz-Cano Ocaña, Antonio
%T Orderings and maximal ideals of rings of analytic functions.
%D 2005
%@ 1088-6826
%U https://hdl.handle.net/20.500.14352/49882
%X 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.
%~