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Extensions séparées et immédiates de corps valués

Published online by Cambridge University Press:  12 March 2014

Françoise Delon
Françoise Delon*
Affiliation:
U. E. R. de Mathématique et Informatique, Université Paris-VII, 75251 Paris, France
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Abstract

Baur a défini la notion d'extension séparée de corps valués et montré que toute extension d'un corps maximal est séparée. Nous prouvons que, si (K, υ) est henselien et de caractéristique résiduelle nulle, alors (K, υ) ⊂ (L, w) est séparée ssi L est linéairement disjoint sur K de toute extension immédiate de K.

Separated and immediate extensions of valued fields. The notion of separated extension of valued fields was introduced by Baur. He showed that extensions of maximal fields are separated. We prove that, when (K, υ) is Henselian with residual characteristic 0, then (K, υ) ⊂ (L, w) is separated iff L is linearly disjoint over K from each immediate extension of K.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 2 , June 1988 , pp. 421 - 428
Copyright
Copyright © Association for Symbolic Logic 1988

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References

RÉFÉRENCES

[Bl] Baur, W., Die Theorie der Paare reell abgeschlossener Körper, Logic and algorithmic (in honour of E. Specker), Monographies de L'Enseignement Mathématique, no. 30, Université de Genève, Geneva, 1982, pp. 25–34.Google Scholar
[B2] Baur, W., On the theory of pairs of real closed fields. II, this Journal, vol. 47 (1982), pp. 669–679.Google Scholar
[CK] Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[D] Delon, F., Quelques propriétés des corps valués en théorie des modèles, Thèse de doctorat d'état, Université Paris-VII, Paris, 1982.Google Scholar
[K] Kuhlmann, F.-V., Defectless extensions of valued fields, Manuscript, Heidelberg, 1987.Google Scholar
[L] Lang, S., Introduction to algebraic geometry, Interscience, New York, 1958.Google Scholar
[Le] Leloup, G., Théories complètes de corps valués henseliens, Thèse de 3ème cycle, Université Paris-VII, Paris, 1985.Google Scholar
[R] Ribenboim, P.. Théorie des valuations, Les Presses de l'Université de Montréal, Montréal, 1964.Google Scholar