Resumen de Extending automorphisms to the rational fractions field

Adrián Llerena Ruiz, F. F. Rodríguez

• 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 with an unique archimedean ordering. We have introduced an apparently stronger type of extension property, simplifying some techniques and broadening the results.