Abstract
Let K be a chainable field, which means a field admitting orderings of exact level 2n for any n≥1, from [G1] and [G2] we know that in such a field there exists α ∈ K such that α2 ∉ Σ K4; we then define the notion of α-chain of orderings and use it to obtain explicit formulas for orderings of exact level 2n in some special fields. We also obtain for some chain-closed fields a new extension of Hilbert's 17th problem.
Keywords
- Holomorphy Ring
- Chainable Field
- Real Holomorphy Ring
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© 1992 Springer-Verlag
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Gondard-Cozette, D. (1992). Sur les ordres de niveau 2n et sur une extension du 17ème probleme de Hilbert. In: Coste, M., Mahé, L., Roy, MF. (eds) Real Algebraic Geometry. Lecture Notes in Mathematics, vol 1524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084625
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DOI: https://doi.org/10.1007/BFb0084625
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