Publication

Valuative trees over valued fields

Journal Article (2023)

Journal

Journal of Algebra

Pages

71-114

Volume

614

Doc link

https://doi.org/10.1016/j.jalgebra.2022.09.014

File

Download the digital copy of the doc pdf document

Authors

Abstract

For an arbitrary valued field (K,v) and a given extension (as ordered groups) Λ of its value group, we analyze the structure of the tree formed by all Λ-valued extensions of v to the polynomial ring K[x]. As an application, we find a model for the tree of all equivalence classes of valuations on K[x](without fixing their value group), whose restriction to K is equivalent to v.

Categories

optimisation, pattern recognition.

Author keywords

Valuative tree, key polynomial, Mac Lane-Vaquié chain

Scientific reference

M. Alberich-Carramiñana, J. Guàrdia, E. Nart and J. Roé. Valuative trees over valued fields. Journal of Algebra, 614: 71-114, 2023.