Extending valuations to algebraic division algebras
M. Mahdavi-Hezavehi · Communications in Algebra · 1994
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 dim$sub:Fesub:K < ∞, (ii) Z(D′) C V*.