2026-07-31T10:18:46Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/646282024-03-01T14:46:01Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Gamboa Mutuberria, José Manuel
2023-06-21T02:01:45Z
2023-06-21T02:01:45Z
1987
0021-8693
10.1016/0021-8693(87)90033-0
https://hdl.handle.net/20.500.14352/64628
http://www.sciencedirect.com/science/journal/00218693
http://www.sciencedirect.com
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 < b, then f takes on its maximum value at some c 2 [a, b]; (3) K is real closed.
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.
Some New Results On Ordered Fields
journal article