The Defektsatz for Central Simple Algebras

DOI10.2307/2153937zbMath0761.16007OpenAlexW4236923255MaRDI QIDQ4006679

Joachim Graeter

Publication date: 26 September 1992

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2153937

zbMATH Keywords

ramification indexcentral simple algebrasintersection propertyDubrovin valuation ringsdivision algebraBezout ordersOstrowski's theoremHenselizationresidue degreenumber of extensionsDefektsatzmatrix sizetotal extensions

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Valuations and their generalizations for commutative rings (13A18) Noncommutative local and semilocal rings, perfect rings (16L30) Extension theory of commutative rings (13B02) Finite-dimensional division rings (16K20) Divisibility, noncommutative UFDs (16U30) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) General valuation theory for fields (12J20)

Related Items (9)

Integral semihereditary orders, extremality, and Henselization ⋮ Integral semihereditary orders inside a Bézout maximal order ⋮ Extending rings of Prüfer type in central simple algebras. ⋮ On the intersection property of Dubrovin valuation rings ⋮ Value functions and associated graded rings for semisimple algebras ⋮ Value functions and Dubrovin valuation rings on simple algebras ⋮ On extending Prüfer rings in central simple algebras ⋮ Correspondences between valued division algebras and graded division algebras ⋮ A classification of prime segments in simple artinian rings

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