Displaying similar documents to “On Trace Forms of Algebraic Number Fields.”

Reduction of semialgebraic constructible functions

Ludwig Bröcker (2005)

Annales Polonici Mathematici

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Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.

On ruled fields

Jack Ohm (1989)

Journal de théorie des nombres de Bordeaux

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Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.