Abstract
In general, the value groups and the residue fields do not suffice to classify the algebraic henselian extensions of a valued fieldK, up to isomorphism overK. We define a stronger, yet natural structure which carries information about additive and multiplicative congruences in the valued field, extending the information carried by value groups and residue fields. We discuss the cases where these “mixed structures” give a solution of the classification problem.
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Basarab, S.A., Kuhlmann, FV. An isomorphism theorem for henselian algebraic extensions of valued fields. Manuscripta Math 77, 113–126 (1992). https://doi.org/10.1007/BF02567049
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DOI: https://doi.org/10.1007/BF02567049