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On the spectra of rings of semialgebraic functions

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dc.contributor.authorFernando Galván, José Francisco
dc.contributor.authorGamboa Mutuberria, José Manuel
dc.date.accessioned2023-06-20T00:16:44Z
dc.date.available2023-06-20T00:16:44Z
dc.date.issued2012
dc.description.abstractIn this article we study the most significant algebraic, topological and functorial properties of the Zariski and maximal spectra of rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipGAAR Español
dc.description.sponsorshipProyecto Santander-Complutense
dc.description.sponsorshipGAAR Grupos UCM
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16469
dc.identifier.doihttp://dx.doi.org10.1007/s13348-011-0041-0
dc.identifier.issn0010-0757
dc.identifier.officialurlhttp://www.springerlink.com/content/403403218426u17m/fulltext.pdf
dc.identifier.relatedurlhttp://www.springerlink.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/42319
dc.issue.number3
dc.journal.titleCollectanea mathematica
dc.language.isoeng
dc.page.final331
dc.page.initial299
dc.publisherSpringer
dc.relation.projectIDMTM2008-00272
dc.relation.projectIDPR34/07-15813
dc.relation.projectID910444
dc.rights.accessRightsrestricted access
dc.subject.cdu512
dc.subject.keywordSemialgebraic function
dc.subject.keywordSemialgebraic set
dc.subject.keywordZariski spectrum
dc.subject.keywordReal spectrum
dc.subject.keywordMaximal spectrum
dc.subject.keywordFunctoriality
dc.subject.keywordLocal compactness
dc.subject.keywordPieces
dc.subject.keywordSemialgebraic depth
dc.subject.keywordz-ideal
dc.subject.ucmFunciones (Matemáticas)
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleOn the spectra of rings of semialgebraic functions
dc.typejournal article
dc.volume.number63
dcterms.referencesBochnak, J., Coste, M., Roy, M.-F.: Real Algebraic Geometry. Ergeb. Math., vol. 36. Springer, Berlin (1998) Bourbaki, N.: General Topology, chapters 1–4. Elements of Mathematics. Springer, Berlin (1989) Birkhoff G., Pierce R.S.: Lattice-ordered rings. An. Acad. Brasil. Ci. 28, 41–69 (1956) Cherlin G.-L., Dickmann M.A.: Real closed rings. I. Residue rings of rings of continuous functions. Fund. Math. 126(2), 147–183 (1986) Cherlin G.-L., Dickmann M.A.: Real closed rings. II. Model theory. Ann. Pure Appl. Log. 25(3), 213–231 (1983) Delfs H., Knebusch M.: Separation, retractions and homotopy extension in semialgebraic spaces. Pac. J. Math. 114(1), 47–71 (1984) Fernando, J.F.: On chains of prime ideals in rings of semialgebraic functions. http://www.mat.ucm.es/~josefer/pdfs/preprint/chains.pdf (preprint RAAG, 2010) Fernando, J.F.: On distinguished points of the remainder of the semialgebraic Stone–Čech compactification of a semialgebraic set. http://www.mat.ucm.es/~josefer/pdfs/preprint/remainder.pdf (preprint RAAG, 2010) Fernando, J.F.: On the fibers of semialgebraic spectral maps. http://www.mat.ucm.es/~josefer/pdfs/preprint/fibers.pdf (preprint RAAG, 2010) Fernando, J.F., Gamboa, J.M.: On Łojasiewicz’s inequality and the Nullstellensatz for rings of semialgebraic functions. http://www.mat.ucm.es/~josefer/pdfs/preprint/null-loj.pdf (preprint RAAG, 2010) Fernando, J.F., Gamboa, J.M.: On the Krull dimension of rings of semialgebraic functions. http://www.mat.ucm.es/~josefer/pdfs/preprint/dim.pdf (preprint RAAG, 2010) Fernando, J.F., Gamboa, J.M.: On Banach-Stone type theorems in the semialgebraic setting. http://www.mat.ucm.es/~josefer/pdfs/preprint/homeo.pdf (preprint RAAG, 2010) Fernando, J.F., Gamboa, J.M.: On the semialgebraic Stone–Čech compactification of a semialgebraic set. Transactions of AMS. http://www.ams.org/cgi-bin/mstrack/accepted_papers?jrnl=tran (2010, accepted) Gillman, L., Jerison, M.: Rings of continuous functions. The University Series in Higher Nathematics, vol. 1. D. Van Nostrand Company, Inc., Princeton (1960) De Marco G., Orsatti A.: Commutative rings in which every prime ideal is contained in a unique maximal ideal. Proc. Am. Math. Soc. 30(3), 459–466 (1971) Schwartz, N.: Real closed spaces. Ordered fields and real algebraic geometry (Boulder, Colo., 1983). Rocky Mt. J. Math. 14(4), 971–972 (1984) Schwartz, N.: The basic theory of real closed spaces. Mem. Am. Math. Soc. 77(397) (1989) Stasica J.: Smooth points of a semialgebraic set. Ann. Polon. Math. 82(2), 149–153 (2003)
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relation.isAuthorOfPublication.latestForDiscovery499732d5-c130-4ea6-8541-c4ec934da408

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