Título: | Some New Results On Ordered Fields |
Autores: | Gamboa, J. M. |
Tipo de documento: | texto impreso |
Editorial: | Academic Press, 1987 |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Topología , Tipo = Artículo |
Resumen: |
The author shows there is a non-Archimedean ordering of the field R(x, y), where x and y are algebraically independent over K, for which the identity is the only order-preserving automorphism. The author proves the partly known result that the following statements about an ordered field K are equivalent: (1) each polynomial in K[x] satisfies the intermediate value theorem; (2) if f 2 K[x] and a A (not necessarily ordered) field K is said to have the extension property if each automorphism of K(x), where x is transcendental over K, is an extension of an automorphism of K. The author gives sufficient conditions for a field to have the the extension property. For example, a field has the extension property if, for some fixed integer n greater than two, each polynomial xn?ax?1, a 2 K, has a root in K. |
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