Exercise 32, § 7

Extend the results of no. 10 to the case where $A$ is a non-commutative ring admitting a field of left fractions $K$ (I, § 9, Exercise 15). (Note that if $\xi_i$ ($1 \leq i \leq n$) are elements of $K$, there exists an $\alpha \neq 0$ in $A$ such that all the $\alpha \xi_i$ belong to $A$.)