Open AccessOrderings and maximal ideals of rings of analytic functions
Author(s) -
A. Dı́az-Cano
Publication year - 2005
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-05-07848-2
Subject(s) - annotation , algorithm , type (biology) , semantics (computer science) , computer science , mathematics , artificial intelligence , programming language , biology , ecology
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