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Orderings and maximal ideals of rings of analytic functions.

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dc.contributor.authorDíaz-Cano Ocaña, Antonio
dc.date.accessioned2023-06-20T09:33:08Z
dc.date.available2023-06-20T09:33:08Z
dc.date.issued2005
dc.description.abstractWe 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.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipEuropean Community’s Human Potential Programme
dc.description.sponsorshipRAAG
dc.description.sponsorshipGAAR
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15040
dc.identifier.doi10.1090/S0002-9939-05-07848-2
dc.identifier.issn1088-6826
dc.identifier.officialurlhttp://www.ams.org/journals/proc/2005-133-10/S0002-9939-05-07848-2/S0002-9939-05-07848-2.pdf
dc.identifier.relatedurlhttp://www.ams.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/49882
dc.issue.number10
dc.journal.titleProceedings of the American Mathematical Society
dc.language.isoeng
dc.page.final2828
dc.page.initial2821
dc.publisherAmerica Mathematical Society
dc.relation.projectIDHPRN-CT-2001-00271
dc.relation.projectIDBFM2002-04797
dc.rights.accessRightsopen access
dc.subject.cdu512.7
dc.subject.keywordReal analytic sets
dc.subject.keywordAnalytic functions
dc.subject.keywordMaximal ideal
dc.subject.keywordUltrafilters
dc.subject.keywordorderings.
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleOrderings and maximal ideals of rings of analytic functions.
dc.typejournal article
dc.volume.number133
dcterms.referencesC. Andradas, E. Becker. A note on the real spectrum of analytic functions on an analytic manifold of dimension one. Lect. Notes Math. 1420 (1990), 1–21. C. Andradas, L. Br¨ocker, J. M. Ruiz. Constructible sets in real geometry. Springer- Verlag, Berlin, 1996. J. Bochnak, M. Coste, M.-F. Roy. Real Algebraic Geometry. Springer-Verlag, Berlin, 1998. A. Castilla. Sums of 2n-th powers of meromorphic functions with compact zero set. Lect. Notes Math. 1524 (1991), 174–177. A. Castilla. Artin-Lang property for analytic manifolds of dimension two. Math. Z. 217 (1994), 5–14. A. Castilla. Propiedad de Artin-Lang para variedades anal´ıticas de dimensi´on dos. Ph. D. Thesis, Universidad Complutense de Madrid (1994). A. D´ıaz-Cano, C. Andradas. Complexity of global semianalytic sets in a real analytic manifold of dimension 2. J. reine angew. Math. 534 (2001), 195–208. L. Gillman, M. Jerison. Rings of continuous functions. Van Nostrand, Princeton, 1960. M. Hirsch. Differential Topology. Springer-Verlag, 1976. P. Jaworski. The 17-th Hilbert problem for noncompact real analytic manifolds. Lecture Notes Math. 1524 (1991), 289–295. K. Kurdyka, G. Raby. Densit´e des ensembles sous-analytiques. Ann. Inst. Fourier 39(1989), 753–771.
dspace.entity.typePublication
relation.isAuthorOfPublication134ad262-ecde-4097-bca7-ddaead91ce52
relation.isAuthorOfPublication.latestForDiscovery134ad262-ecde-4097-bca7-ddaead91ce52

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