A Ganzstellensatz for Semialgebraic Sets and a Boundedness Criterion for Rational Functions. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Lavi, Noa
• Is Part Of: Communications in algebra. Volume 44:Issue 1(2016)
• Page Start: 26
• Page End: 39
• Publication Date: 2016-01-02
• Subjects: Algebra -- Model theory -- Real algebraic geometry -- Valuation theory; Primary 14P10 -- Secondary 03C64 -- 12J20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2014.930473
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Let ⟨ K, ν ⟩ be a real closed valued field, and let S ⊆ K n be an open semialgebraic set. Using tools from model theory, we find an algebraic characterization of rational functions which admit, on S, only values in the valuation ring. We use this result to deduce a criterion for a rational function to be bounded on an open semialgebraic subset of some irreducible variety over a real closed field or over an ordered field which is dense in its real closure.