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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Extending valuations to finite-dimensional division algebras


Author: Adrian R. Wadsworth
Journal: Proc. Amer. Math. Soc. 98 (1986), 20-22
MSC: Primary 16A39; Secondary 12E15
MathSciNet review: 848866
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Abstract: Let $ D$ be a division algebra finite dimensional over its center $ F$. It is shown that a (Krull) valuation $ v$ on $ F$ extends to a valuation on $ D$ iff $ \upsilon $ extends uniquely to each commutative field $ K$ with $ F \subseteq K \subseteq D$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0848866-8
PII: S 0002-9939(1986)0848866-8
Article copyright: © Copyright 1986 American Mathematical Society