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Value functions on central simple algebras


Author: Patrick J. Morandi
Journal: Trans. Amer. Math. Soc. 315 (1989), 605-622
MSC: Primary 16A10; Secondary 11S45, 12J10
DOI: https://doi.org/10.1090/S0002-9947-1989-0986697-6
MathSciNet review: 986697
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Abstract: In this paper we study noncommutative valuation rings as defined by Dubrovin. While there is in general no valuation associated to a Dubrovin valuation ring, we show that there is a value function associated to any Dubrovin valuation ring integral over its center. By using value functions we obtain information on Dubrovin valuation rings in a tensor product, both generalizing and giving a much simpler proof of a result about valued division algebras. By being able to work directly with central simple algebras we gain new information about division algebras over Henselian fields.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0986697-6
Article copyright: © Copyright 1989 American Mathematical Society

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