“School of Mathematics”
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| Paper IPM / M / 161 |
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| Abstract: | |
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Let D be a division algebra algebraic
over its centre F. Given a (Krull) valuation v on F, denote by V its valuation ring. It is shown that v extends to a valuation on D if and only if (i) v extends uniquely to each commutative subfield K of D with dimF K < ∞, (ii) Z(D′) ⊂ V*.
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