Remarks on existentially closed fields and diophantine equations
Paulo Ribenboim (1984)
Rendiconti del Seminario Matematico della Università di Padova
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Paulo Ribenboim (1984)
Rendiconti del Seminario Matematico della Università di Padova
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Fernando Fernández Rodríguez, Agustín Llerena Achutegui (1991)
Extracta Mathematicae
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We say that a field K has the Extension Property if every automorphism of K(X) extends to an automorphism of K. J.M. Gamboa and T. Recio [2] have introduced this concept, naive in appearance, because of its crucial role in the study of homogeneity conditions in spaces of orderings of functions fields. Gamboa [1] has studied several classes of fields with this property: Algebraic extensions of the field Q of rational numbers; euclidean, algebraically closed and pythagorean fields; fields...
Jan-Hendrik Evertse (1986)
Acta Arithmetica
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Keng-Teh Tan (1975)
Publications de l'Institut Mathématique
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Nicolae Popescu, Constantin Vraciu (1985)
Rendiconti del Seminario Matematico della Università di Padova
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Barry Green (1991)
Journal de théorie des nombres de Bordeaux
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F. S. Cater (2002)
Czechoslovak Mathematical Journal
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In this note we study fields with the property that the simple transcendental extension of is isomorphic to some subfield of but not isomorphic to . Such a field provides one type of solution of the Schröder-Bernstein problem for fields.
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.
Victor Alexandru, Nicolae Popescu (1994)
Rendiconti del Seminario Matematico della Università di Padova
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