Andradas Heranz, Carlos and Gamboa Mutuberria, José Manuel (1984) A note on projections of real algebraic varieties. Pacific Journal of Mathematics, 115 . pp. 1-11. ISSN 0030-8730
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Real algebraic varieties; Regularly closed semialgebraic set; Clopen subset; Space of orders of rational functions |
| Subjects: | Sciences > Mathematics > Algebraic geometry |
| ID Code: | 14843 |
| 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). |
| Deposited On: | 18 Apr 2012 12:29 |
| Last Modified: | 05 Apr 2013 17:29 |
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