Let $D$ be a division ring. I have in mind the following result.
Theorem. For every automorphism $f$ of $D$, there is a division ring $E$ extending $D$ such that $f$ extends to an inner automorphism of $E$.
Q1. Is the Theorem correct? Any reference?
Q2. If $f$ fixes the centre of $D$ pointwise, can $E$ be chosen so as to have the same centre as $D$?