Journal title
Proceedings of the Edinburgh Mathematical Society
DOI
10.1017/S0013091516000341
Issue
3
Volume
60
Last updated
2024-03-11T15:25:50.97+00:00
Page
665-687
Abstract
We study the question of which Henselian fields admit definable Henselian valuations (with or without parameters). We show that every field that admits a Henselian valuation with non-divisible value group admits a parameter-definable (non-trivial) Henselian valuation. In equicharacteristic 0, we give a complete characterization of Henselian fields admitting a parameter-definable (non-trivial) Henselian valuation. We also obtain partial characterization results of fields admitting-definable (non-trivial) Henselian valuations. We then draw some Galois-theoretic conclusions from our results.
Symplectic ID
505668
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Publication type
Journal Article
Publication date
10 Jan 2017