MacLane-Vaquié chains of valuations on a polynomial ring

DOI10.2140/pjm.2021.311.165zbMath1485.13012arXiv1911.01714OpenAlexW2986942152MaRDI QIDQ2057575

Enric Nart Viñals

Publication date: 7 December 2021

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.01714

zbMATH Keywords

graded algebrakey polynomial

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) General valuation theory for fields (12J20)

Related Items (11)

Rigidity of valuative trees under Henselization ⋮ The defect formula ⋮ Graded rings associated to valuations and direct limits ⋮ Geometric parametrization of valuations on a polynomial ring in one variable ⋮ MacLane-Vaquié chains and valuation-transcendental extensions ⋮ Valuations with an infinite limit-depth ⋮ Computation of residual polynomial operators of inductive valuations ⋮ Valuations on \(K[x\) approaching a fixed irreducible polynomial] ⋮ On truncations of valuations ⋮ Valuative trees over valued fields ⋮ Abstract key polynomials and MacLane-Vaquié chains

Cites Work

• All valuations on K(X)
• Key polynomials over valued fields
• Defectless polynomials over Henselian fields and inductive valuations
• Admissible family of valuations and defect of an extension.
• Valuations in algebraic field extensions
• Extension d’une valuation
• Value groups, residue fields, and bad places of rational function fields
• A Construction for Absolute Values in Polynomial Rings

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