On a division ring with discrete valuation (Q1344198)

A division ring \(A\) with non-trivial valuation \(\nu\) has the completion \(A^*\) with respect to the \(\nu\)-topology, which is also a division ring. If \(B\) is a division subring of \(A\), then the closure \(B^*\) of \(B\) in \(A^*\), with respect to the \(\nu\)-topology, is isomorphic to the completion of \(B\) as a topological ring. The purpose of the author's paper is to show that \(B^*\) coincides with the double centralizer of \(B\) in \(A^*\) for each division \(C\)-subalgebra \(B\) of \(A\) (where \(C\) is the center of \(A\)), when \(A\) is finite over \(C\) and \(\nu\) is discrete.