The group of units of a free product of rings

The main theorem asserts that the multiplicative group of a free product of rings, all of which satisfy the condition $xy=1\Rightarrow yx=1$, with the amalgamated skew field $\Lambda$, is a free product of a certain family of its subgroups with an amalgamated subgroup $\Lambda\setminus\{0\}$. As an application a ring $R$ is indicated for which the group $\operatorname{GE}_n(R)$ is a nontrivial free factor of $\operatorname{GL}_n(R)$ ($n$ being any natural number greater than one).
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