A note on projections of real algebraic varieties.
| dc.contributor.author | Andradas Heranz, Carlos | |
| dc.contributor.author | Gamboa Mutuberria, José Manuel | |
| dc.date.accessioned | 2023-06-21T02:01:29Z | |
| dc.date.available | 2023-06-21T02:01:29Z | |
| dc.date.issued | 1984 | |
| dc.description.abstract | We prove that any regularly closed semialgebraic set of R", where R is any real closed field and regularly closed means that it is the closure of its interior, is the projection under a finite map of an irreducible algebraic variety in some Rn + k. We apply this result to show that any clopen subset of the space of orders of the field of rational functions K= R(X1,...iXn) is the image of the space of orders of a finite extension of K. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14843 | |
| dc.identifier.issn | 0030-8730 | |
| dc.identifier.officialurl | http://projecteuclid.org/pjm | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64608 | |
| dc.journal.title | Pacific Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 11 | |
| dc.page.initial | 1 | |
| dc.publisher | Pacific Journal of Mathematics | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Real algebraic varieties | |
| dc.subject.keyword | Regularly closed semialgebraic set | |
| dc.subject.keyword | Clopen subset | |
| dc.subject.keyword | Space of orders of rational functions | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | A note on projections of real algebraic varieties. | |
| dc.type | journal article | |
| dc.volume.number | 115 | |
| dcterms.references | G. W. Brumfiel, Partially ordered fields and semialgebraic geometry, London Math. Soc. Lect. Notes, 37 (1979). M. Coste and M. F. Roy, La topologie du spectre reel, Contemporary Math., 8 (1982), 27-59. D. W. Dubois and T. Recio, Order extensions and real algebraic geometric, Contemporary Math., 8 (1982), 265-288. R. Elman, T. Y. Lam and A. Wadsworth, Orderings under field extensions, J. Reine Ang. Math., 306 (1979), 7-27. R. Hartshorne, Algebraic Geometry, G.T.M. no. 52, Springer Verlag, (1977). T. S. Motzkin, The Real Solution Set of a System of Algebraic Inequalities, Inequalities II, Academic Press (1970). A. Prestel, Lectures on Formally Real Fields, I.M.P.A. no. 25, (1975). T. Recio, Una descomposicibn de un conjunto semialgebraico, Actas V Congreso de Matematicas de expresiόn Latina. Mallorca, Spain, (1977). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a74c23fe-4059-4e73-806b-71967e14ab67 | |
| relation.isAuthorOfPublication | 8fcb811a-8d76-49a2-af34-85951d7f3fa5 | |
| relation.isAuthorOfPublication.latestForDiscovery | a74c23fe-4059-4e73-806b-71967e14ab67 |
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