Real Algebraic and Analytic Geometry
Submission: 2005, April 17.
We prove a criterion for an element of a commutative ring to be contained in an archimedean subsemiring. It can be used to investigate the question whether nonnegativity of a polynomial on a compact semialgebraic set can be certified in a certain way. In case of (strict) positivity instead of nonnegativity, our criterion simplifies to classical results of Stone, Kadison, Krivine, Handelman, Schmüdgen et al. As an application of our result, we give a new proof of the following result of Handelman: If an odd power of a real polynomial in several variables has only nonnegative coefficients, then so do all sufficiently high powers.
Mathematics Subject Classification (2000): 13J25, 13J30, 16Y60, 26C99, 54H10.
Keywords and Phrases: nonnegative polynomial, semiring, preprime, preorder, preordering, archimedean, Real Representation Theorem, Kadison-Dubois Theorem.
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