Algebraic independence of elements in immediate extensions of valued fields

DOI10.1016/j.jalgebra.2014.10.050zbMath1359.12004arXiv1304.1381OpenAlexW2963704012MaRDI QIDQ2254143

Franz-Viktor Kuhlmann, Anna Blaszczok

Publication date: 4 February 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.1381

zbMATH Keywords

algebraic independencevalued fieldimmediate extensionuniqueness of maximal immediate extensions

Mathematics Subject Classification ID

Non-Archimedean valued fields (12J25) Valued fields (12J10)

Related Items (11)

On the non-uniqueness of maximal purely wild extensions ⋮ Valuation theory and its applications. Abstracts from the workshop held October 26 -- November 1, 2014. ⋮ Tate algebras and Frobenius non-splitting of excellent regular rings ⋮ Distances of elements in valued field extensions ⋮ Density of composite places in function fields and applications to real holomorphy rings ⋮ On maximal immediate extensions of valued fields ⋮ Tame key polynomials ⋮ On the behaviour of Brauer \(p\)-dimensions under finitely-generated field extensions. ⋮ Infinite towers of Galois defect extensions of Kaplansky fields ⋮ Valuations on rational function fields that are invariant under permutation of the variables ⋮ Corrections and notes to “Value groups, residue fields and bad places of rational function fields”

Cites Work

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• A classification of Artin-Schreier defect extensions and characterizations of defectless fields
• Every place admits local uniformization in a finite extension of the function field
• Immediate and purely wild extensions of valued fields
• Valuation theory
• The relative approximation degree in valued function fields
• Maximal fields with valuations. I, II
• Elimination of ramification I: The generalized stability theorem
• Note on a result of Krull
• Nonuniqueness of immediate maximal extensions of a valuation.
• Abhyankar places admit local uniformization in any characteristic
• Value groups, residue fields, and bad places of rational function fields
• Valuation theoretic and model theoretic aspects of local uniformization
• Valued Fields

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