Algebraic systems of quadratic forms of number fields and function fields.
Martin Krüskemper (1989)
Manuscripta mathematica
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Martin Krüskemper (1989)
Manuscripta mathematica
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John Smith (1975)
Acta Arithmetica
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Albrecht Fröhlich (1960)
Mathematische Zeitschrift
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Dress, Andreas W.M. (1997)
Beiträge zur Algebra und Geometrie
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Manohar L. Madan (1976/77)
Mathematische Zeitschrift
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Zhongming Tang (1990)
Mathematische Zeitschrift
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Alfred Czogala (1981)
Mathematische Zeitschrift
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Albrecht Fröhlich (1960)
Mathematische Zeitschrift
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Jenna P. Carpenter (1992)
Mathematische Zeitschrift
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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.
M.E. Alonso, M.F. Roy (1987)
Mathematische Zeitschrift
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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.
Alberto Baider, Richard Churchill (1988)
Mathematische Zeitschrift
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