A note on projections of real algebraic varieties.



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Andradas Heranz, Carlos and Gamboa, J. M. (1984) A note on projections of real algebraic varieties. Pacific Journal of Mathematics, 115 . pp. 1-11. ISSN 0030-8730

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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
Deposited On:18 Apr 2012 10:29
Last Modified:07 Aug 2018 11:46

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