Valuation rings in Ore extensions

DOI10.1006/JABR.2000.8484zbMath0970.16014OpenAlexW2032906226MaRDI QIDQ5925848

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Publication date: 15 October 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8484

zbMATH Keywords

endomorphismsextensionsinner automorphismsskew fields of fractionsskew polynomial ringstotal subringsvaluation ringsvalued skew fields

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Infinite-dimensional and general division rings (16K40)

Related Items (7)

TOTAL VALUATION RINGS OFK(X, σ) CONTAININGK ⋮ Primes of Gauss Extensions Over Crossed Product Algebras ⋮ Total valuation rings of Ore extensions. ⋮ A classification of graded extensions in a skew Laurent polynomial ring. ⋮ Gauss extensions and total graded subrings for crossed product algebras. ⋮ Noncommutative valuation rings of the quotient Artinian ring of a skew polynomial ring. ⋮ A classification of graded extensions in a skew Laurent polynomial ring. II.

Cites Work

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• Bewertungen nicht kommutativer Körper
• Extensions of chain rings
• All valuations on K(X)
• Valuation rings in finite-dimensional division algebras
• Simple transcendental extensions of valued fields. III: The uniqueness property
• Untersuchungen zur arithmetischen Theorie der Körper. (Die Theorie der Teilbarkeit in allgemeinen Körpern. I-III.)
• A Structure Theorem for Simple Transcendental Extensions of Valued Fields
• A uniqueness problem in simple transcendental extensions of valued fields
• Prime Segments of Skew Fields
• Valuations, Primes and Irreducibility in Polynomial Rings and Rational Function Fields
• Finite-Dimensional Division Algebras over Fields

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