Verbal subgroups and subalgebras in skew fields. (Q816639)

Let \(D\) be an arbitrary skew field with central subfield \(K\). The author shows that \(D\) can be embedded in a skew field \(\Delta\) such that \(w(\Delta)=\Delta\) for any nonempty Lie word \(w\) on a set of variables \(y_1,y_2,\dots\) with coefficients in \(K\). Furthermore, for every nonempty word \(v=x_1^{\epsilon_1}x_2^{\epsilon_2}\cdots x_n^{\epsilon_n}\) with \(\epsilon_1,\dots,\epsilon_n\in\{-1,1\}\), the multiplicative group \(\Delta^*\) is such that \(w(\Delta^*)=\Delta^*\).