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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

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