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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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.
|Uncontrolled Keywords:||Real algebraic varieties; Regularly closed semialgebraic set; Clopen subset; Space of orders of rational functions|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
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|Deposited On:||18 Apr 2012 10:29|
|Last Modified:||06 Feb 2014 10:10|
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