I know that the units of $\mathbb{F}_q[T] \subset \mathbb{F}_q(T)$ are the constant non-zero polynomials, of which are there $q-1$, and you can think of these as being in analogy with the units $\pm1$ in $\mathbb{Z}\subset \mathbb{Q}$.
If $F$ is a finite extension of $\mathbb{F}_q(T)$, with integer ring $A$, so the fraction field of $A$ is $F$. Do we know the rank of the unit group of $A$? So we know the size of the unit group $A$? Is something like Dirichlet's unit theorem true in this setting?