Aviso: Por labores de mantenimiento y mejora del repositorio, el martes día 1 de Julio, Docta Complutense no estará operativo entre las 9 y las 14 horas. Disculpen las molestias.
 

On rings of semialgebraic functions

dc.contributor.authorGamboa Mutuberria, José Manuel
dc.contributor.authorRuiz Sancho, Jesús María
dc.date.accessioned2023-06-20T16:52:43Z
dc.date.available2023-06-20T16:52:43Z
dc.date.issued1991
dc.description.abstractThe authors study some properties of the ring of abstract semialgebraic functions over a constructible subset of the real spectrum of an excellent ring. To be more precise, let X be a constructible subset of the real spectrum of a ring A. The ring S(X) of abstract semialgebraic functions over X was introduced bz N. Schwartz [see Mem. Am. Math. Soc. 397 (1989; Zbl 0697.14015)], as a generalization of continuous functions with semialgebraic graph to the context of real spectra. Unfortunately the utility of this functions is not yet quite established. The main result of the paper states that if A is excellent, the Krull dimension of S(X) equals the dimension of X (defined as the maximum of the heights of the supports of points lying in X), which in turn, as J. M. Ruiz showed in C. R. Acad. Sci. Paris, S´er. I 302, 67-69 (1986; Zbl 0591.13017) coincides with its topological dimension. This was first shown by M. Carral and M. Coste [J. Pure Appl. Algebra 30, 227-235 (1983; Zbl 0525.14015)] for the particular case of X being a ‘true’ semialgebraic subset which is locally closed, and the result extends readily to abstract locally closed constructible sets. Then the authors use the compactness of the constructible topology of real spectra and the properties of excellent rings to reduce the general case to the locally closed one. The paper finishes by characterizing the finitely generated prime ideals of S(X), namely they are the ideals of the open constructible points of X whose closure in X is open of dimension 6= 1.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15435
dc.identifier.doi10.1007/BF02571359
dc.identifier.issn0025-5874
dc.identifier.officialurlhttp://www.springerlink.com/content/j00g08123407v6t5/
dc.identifier.relatedurlhttp://www.springerlink.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57305
dc.issue.number4
dc.journal.titleMathematische Zeitschrift
dc.page.final532
dc.page.initial527
dc.publisherSpringer Verlag
dc.rights.accessRightsmetadata only access
dc.subject.cdu512.7
dc.subject.keywordsemialgebraic functions
dc.subject.keywordconstructible subset of the real spectrum of an excellent ring
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleOn rings of semialgebraic functions
dc.typejournal article
dc.volume.number206
dspace.entity.typePublication
relation.isAuthorOfPublication8fcb811a-8d76-49a2-af34-85951d7f3fa5
relation.isAuthorOfPublicationf12f8d97-65c7-46aa-ad47-2b7099b37aa4
relation.isAuthorOfPublication.latestForDiscoveryf12f8d97-65c7-46aa-ad47-2b7099b37aa4

Download

Collections