Let $G$ be a simply connected complex Chevalley group and let $T$ be some maximal torus in $G$ with $dimT\geq 2$.

From A note on generators for arithmetic subgroups of algebraic groups by Raghunathan
we have that for $I\lhd\mathbb Z, Γ(I):=\langle U_\phi(I)|\phi\in\Phi \rangle$ is of finite index in $G(\mathbb Z)$, is it also true for $I\lhd\mathbb Z[\alpha]$ that $Γ(I)$ of finite index in $G(\mathbb Z[\alpha])$?

Where:
-$\Phi$ denote the root system of $G$ with respect to $T$.
-$U_\phi$ is the root subgroup corresponding to $\phi\in\Phi$.
-$\alpha$ is an integral element of $\mathbb Z$.
-If $I$ is an ideal of the ring $A$ and $H\leq G$ we mark $H(I):=\{x\in H(A)|x\equiv1(mod\,I)\}$ where $H(A):=H\cap GL_n(A)$.