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...
R. Mason, B. Brindza (1986)
Acta Arithmetica
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Gerhard Niklash (1997)
Collectanea Mathematica
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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.
Maxwell Rosenlight (1969)
Publications Mathématiques de l'IHÉS
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V. Sprindžuk (1974)
Acta Arithmetica
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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.