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An admissible family associated to a valuation of $$K[x]$$. (Famille admise associée à une valuation de $$K[x]$$.) (French) Zbl 1097.13004
Brasselet, Jean-Paul (ed.) et al., Franco-Japanese singularities. Proceedings of the 2nd Franco-Japanese singularity conference, CIRM, Marseille-Luminy, France, September 9–13, 2002. Paris: Société Mathématique de France (ISBN 2-85629-166-X/pbk). Séminaires et Congrès 10, 391-428 (2005).
Summary: Any valuation $$\mu$$ of $$K[x]$$ extending a given valuation $$\nu$$ of $$K$$ gives a construction of an almost unique admissible family of valuations of $$K[x]$$, which converges to $$\mu$$. The study of the set $${\mathcal E}(K[x],\nu)$$ of the valuations or pseudo-valuations extending $$\nu$$ to $$K[x]$$ is then reduced to the study of the set $${\mathcal F}(K[x], \nu)$$ of admissible families. By this way we call define an order on the set $${\mathcal E}(K[x],\nu)$$.
For the entire collection see [Zbl 1061.14001].

##### MSC:
 13A18 Valuations and their generalizations for commutative rings 12J10 Valued fields
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