Let $A$ be an associative algebra over an algebraically closed field $k$. The following theorem holds (see, for instance, Theorem $2.5$ on page $24$ in Introduction to Representation Theory by Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena Yudovina, arXiv:0901.0827).
Theorem: If $V$ is an irreducible finite-dimensional representation of $A$, then the map $\rho: A \to \text{End}(V)$ is surjective.
Question: Let $\mathcal{L}(\Phi, R)$ denote a Chevalley algebra over a (commutative) ring $R$ (with unity) of type $\Phi$. Does an analogous result apply to such an algebra? (If necessary, we may assume that $\Phi$ is an irreducible root system.)
Any help would be greatly appreciated.
