Displaying similar documents to “Note on a variation of the Schröder-Bernstein problem for fields”

Extending automorphisms to the rational fractions field.

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...

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.

The Joly–Becker theorem for * –orderings

Igor Klep, Dejan Velušček (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove the * –version of the Joly–Becker theorem: a skew field admits a * –ordering of level n iff it admits a * –ordering of level n ℓ for some (resp. all) odd ℓ ∈ ℕ . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a * –ordering of higher level also admits a * –ordering of level 1 . Every field that admits a * –ordering of higher level admits a * –ordering of level 1 or 2