Verbal Subgroups and Subalgebras in Skew Fields
by Lichtman, A. I.
Let D be an arbitrary skew field and K a central subfield of D. We prove that D can be embedded in a skew field Δ such that w(Δ)=Δ for every nonempty Lie word w on a set of variables y1,y2,. . . with coefficients in K; moreover, we have for the multiplicative group Δ* that v(Δ*)=Δ* for every nonempty word
$v=x_{1}^{\varepsilon_{1}}x_{2}^{\varepsilon_{2}}\ldots x_{n}^{\varepsilon_{n}}$
(ɛi=±1; i=1,2,. . .,n).
DOI: 10.1007/s10468-005-3570-y
Print publication date: 5/1/2005
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