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On Open And Closed Morphisms Between Semialgebraic Sets

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dc.contributor.authorGamboa Mutuberria, José Manuel
dc.contributor.authorFernando Galván, José Francisco
dc.date.accessioned2023-06-20T00:11:46Z
dc.date.available2023-06-20T00:11:46Z
dc.date.issued2012-04
dc.description.abstractIn this work we study how open and closed semialgebraic maps between two semialgebraic sets extend, via the corresponding spectral maps,to the Zariski and maximal spectra of their respective rings of semialgebraic and bounded semialgebraic functions.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipSpanish GAAR
dc.description.sponsorshipProyecto Santander Complutense
dc.description.sponsorshipGAAR Grupos UCM
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15166
dc.identifier.doi10.1090/S0002-9939-2011-10989-4
dc.identifier.issn0002-9939
dc.identifier.officialurlhttp://www.ams.org/journals/proc/2012-140-04/S0002-9939-2011-10989-4/S0002-9939-2011-10989-4.pdf
dc.identifier.relatedurlhttp://www.ams.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/42170
dc.issue.number4
dc.journal.titleProceedings of the American Mathematical Society
dc.language.isoeng
dc.page.final1219
dc.page.initial1207
dc.publisherAmerican Mathematical Society
dc.relation.projectIDMTM2008-00272, Proyecto Santander Complutense PR34/07-15813 and GAAR Grupos UCM 910444.
dc.relation.projectIDPR34/07-15813
dc.relation.projectID910444.
dc.rights.accessRightsrestricted access
dc.subject.cdu512.7
dc.subject.keywordSemialgebraic function
dc.subject.keywordsemialgebraic set
dc.subject.keywordZariski spectrum
dc.subject.keywordmaximal spectrum
dc.subject.keywordopen and closed maps
dc.subject.keywordproper map
dc.subject.keywordBezoutian
dc.subject.keywordquotient map
dc.subject.keywordSpaces
dc.subject.keywordRings
dc.subject.keywordMathematics
dc.subject.keywordApplied
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleOn Open And Closed Morphisms Between Semialgebraic Sets
dc.typejournal article
dc.volume.number140
dcterms.referencesM.F. Atiyah, I.G. Macdonald: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ontario: 1969. MR0242802 (39:4129) J. Bochnak, M. Coste, M.-F. Roy: Real algebraic geometry. Ergeb. Math. 36, Springer- Verlag, Berlin: 1998. MR1659509 (2000a:14067) G.W. Brumfiel: Quotient spaces for semialgebraic equivalence relations. Math. Z. 195 (1987), no. 1, 69–78. MR888127 (88i:14015) J.F. Fernando: On chains of prime ideals in rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/chains.pdf J.F. Fernando: On distinguished points of the remainder of the semialgebraic Stone–ˇCech compactification of a semialgebraic set. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/remainder.pdf J.F. Fernando, J.M. Gamboa: On the Krull dimension of rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/dim.pdf J.F. Fernando, J.M. Gamboa: On the spectra of rings of semialgebraic functions. Collectanea Mathematica, to appear. http://www.mat.ucm.es/∼josefer/pdfs/ preprint/spectra.pdf J.F. Fernando, J.M. Gamboa: On Banach-Stone type theorems for semialgebraic sets. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/homeo.pdf J.F. Fernando, J.M. Gamboa: On the semialgebraic Stone–ˇCech compactification of a semialgebraic set. Trans. Amer. Math. Soc. (to appear). http://www.mat.ucm.es/ ∼josefer/pdfs/preprint/mspectra.pdf G. De Marco, A. Orsatti: Commutative rings in which every prime ideal is contained in a unique maximal ideal. Proc. Amer. Math. Soc. 30 (1971), no. 3, 459-466. MR0282962 (44:196) M.-A. Mulero: Algebraic properties of rings of continuous functions. Fund. Math. 149 (1996), no. 1, 55–66. MR1372357 (97c:16038) OPEN AND CLOSED MORPHISMS BETWEEN SEMIALGEBRAIC SETS 1219 V.I. Ponomarev: Open mappings of normal spaces. Dokl. Akad. Nauk SSSR 126 (1959), 716–718. MR0107855 (21:6577) C. Procesi, G. Schwarz: Inequalities defining orbit spaces. Invent. Math. 81 (1985), no. 3, 539–554. MR807071 (87h:20078) Departamento de ´Algebra, Facultad de Ciencias Matem´aticas, Universidad Complutense de Madrid, 28040 Madrid, Spain E-mail address: josefer@mat.ucm.es Departamento de ´Algebra, Facultad de Ciencias Matem´aticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
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relation.isAuthorOfPublication.latestForDiscovery499732d5-c130-4ea6-8541-c4ec934da408

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