Dubrovin valuation rings and Henselization

DOI10.1007/BF01446437zbMath0642.16016MaRDI QIDQ1101531

Adrian R. Wadsworth

Publication date: 1989

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164510

zbMATH Keywords

valuation ringsramification indexcentral simple algebrasmaximal ordersDubrovin valuation ringsclassical valuation rings of division ringsHenselization of the centerOstrowski-type theoremplaces of simple Artinian ringsresidue degree

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Automorphisms and endomorphisms (16W20) Generalizations of commutativity (associative rings and algebras) (16U80) Valuations and their generalizations for commutative rings (13A18) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Division rings and semisimple Artin rings (16Kxx)

Related Items (29)

Dubrovin valuation rings and v-topologies ⋮ Weakly *-ordered *-fields ⋮ Integral semihereditary orders, extremality, and Henselization ⋮ Integral semihereditary orders inside a Bézout maximal order ⋮ Extending rings of Prüfer type in central simple algebras. ⋮ Witt rings of even degree division algebras over number fields ⋮ Value functions on simple Artinian rings ⋮ The corestriction of central simple algebras with dubrovin valuation rings ⋮ Semi-hereditary orders in a simple artinian ring ⋮ Le gradué d’une algèbre à division valuée ⋮ On the intersection property of Dubrovin valuation rings ⋮ Hereditary orders in the quotient ring of a skew polynomial ring ⋮ On Dubrovin Valuation Rings in Crossed Product Algebras ⋮ Dubrovin valuation properties of skew group rings and crossed products ⋮ Weak crossed-product orders over valuation rings. ⋮ Maximal orders over valuation rings ⋮ A note on valued division algebras ⋮ A Valuation Theory for Nonassociative Quaternion Algebras ⋮ Value Functions on Central Simple Algebras ⋮ Value functions and associated graded rings for semisimple algebras ⋮ Noncommutative valuation rings of the quotient Artinian ring of a skew polynomial ring. ⋮ Value functions and Dubrovin valuation rings on simple algebras ⋮ Integral Dubrovin Valuation Rings ⋮ On extending Prüfer rings in central simple algebras ⋮ Correspondences between valued division algebras and graded division algebras ⋮ An approximation theorem for Dubrovin valuation rings ⋮ Rings of the Morita Contexts and Semihereditary MaximalV-Orders ⋮ A classification of prime segments in simple artinian rings ⋮ Dubrovin valuation skew group rings

Cites Work

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• Valuations on finite-dimensional division algebras and their value groups
• Division algebras over Henselian fields.
• Equivalent forms of Hensel's lemma
• Valuations of skew fields and projective Hjelmslev spaces
• The Brauer group and the center of generic matrices
• The Henselization of a valued division algebra
• Separable algebras over commutative rings
• Cancellation of Azumaya algebras
• Valuation theory
• Invariante Untermoduln des Endomorphismenrings eines Vektorraumes
• Noetherian Pi-Rings
• The Cartan-Brauer-Hua Theorem for Matrix and Local Matrix Rings
• Ostrwoski's theorem for Henselian valued skew fields.
• Extending Valuations to Finite Dimensional Division Algebras

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