An invariant of valuation transcendental extensions and its connection with key polynomials

DOI10.1016/J.JALGEBRA.2024.03.008MaRDI QIDQ6495837

Arpan Dutta

Publication date: 2 May 2024

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

zbMATH Keywords

minimal pairskey polynomialsextension of valuationsvaluation transcendental extensionsMac Lane-Vaquié key polynomials

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Non-Archimedean valued fields (12J25) General valuation theory for fields (12J20)

Cites Work

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• A theorem of characterization of residual transcendental extensions of a valuation
• Abstract key polynomials and comparison theorems with the key polynomials of Mac Lane-Vaquié
• Minimal pairs of definition of a residual transcendental extension of a valuation
• All valuations on K(X)
• Tame fields and tame extensions
• Key polynomials and pseudo-convergent sequences
• Key polynomials and minimal pairs
• On MacLane-Vaquié key polynomials
• On the implicit constant fields and key polynomials for valuation algebraic extensions
• Minimal pairs, minimal fields and implicit constant fields
• Key polynomials over valued fields
• Valuation theory
• Extension d’une valuation
• Value groups, residue fields, and bad places of rational function fields
• Minimal pairs, inertia degrees, ramification degrees and implicit constant fields
• Valued Fields
• On Chains Associated with Elements Algebraic over a Henselian Valued Field
• Tame key polynomials

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