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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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