Abstract

ABSTRACTLet D be a division algebra algebraic over its center F. Given a (Krull) valuation v on F, it is shown that v extends to a valuation on D if and only if for each separable element c∈D′ there exists a valuation w on K: = F(c) extending v on F such that , where D′ is the derived group of D* and W* is the unit group of the valuation ring W of w.

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