Díaz-Cano Ocaña, Antonio2023-06-202023-06-2020051088-682610.1090/S0002-9939-05-07848-2https://hdl.handle.net/20.500.14352/49882We 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.engjournal articlehttp://www.ams.org/journals/proc/2005-133-10/S0002-9939-05-07848-2/S0002-9939-05-07848-2.pdfhttp://www.ams.org/open access512.7Real analytic setsAnalytic functionsMaximal idealUltrafiltersorderings.Geometria algebraica1201.01 Geometría Algebraica