Extending valuations to finite-dimensional division algebras

Wadsworth, Adrian R.

doi:10.1090/S0002-9939-1986-0848866-8

Extending valuations to finite-dimensional division algebras
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by Adrian R. Wadsworth

Proc. Amer. Math. Soc. 98 (1986), 20-22

DOI: https://doi.org/10.1090/S0002-9939-1986-0848866-8

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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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