  Let $\Phi $ be a Drinfeld $\mathbf{F}_{q}[T]$-module of rank 2, over a finite
field $L$, a finite extension of $n$ degrees for a finite field with $q$
elements $% \mathbf{F}_{q}$. Let $P_{\Phi}(X)=$ $X^{2}-cX+\mu P^{m}$ ($c$ an
element of $% \mathbf{F}_{q}[T]$ and $\mu $ a no null element of
$\mathbf{F}_{q}$, $m$ the degree of the extension $L$ over the field
$\mathbf{F}_{q}[T]/P$, $P$ is a $\mathbf{F}%_{q}[T]$-characteristic of $L$ and
$d$ the degree of the polynomial $P$) the characteristic polynomial, of the
Frobenius $F$ of $L$. We will interested to the structure of finite
$\mathbf{F}_{q}[T]$-module $L^{\Phi}$ deduct by $\Phi $ over $L$ and will proof
our main result, the analogue of Deuring theorem for the elliptic curves : Let
$M=\frac{\mathbf{F}%_{q}[T]}{I_{1}}\oplus \frac{\mathbf{F}_{q}[T]}{I_{2}}$,
where $I_{1}=(i_{1})$,$% I_{2}=(i_{2})$ ($i_{1}$, $i_{2}$ two polynomials of
$\mathbf{F}_{q}[T]$%) and such that : $i_{2}\mid (c-2)$. Then there exists an
ordinary Drinfeld $\mathbf{F}_{q}[T]$% -module $\Phi $ over $L$ of rank 2, such
that : $% L^{\Phi}$ $\simeq M$. We finish by a statistic about the cyclicity of
such structure $L^{\Phi}$, and we prove that is cyclic only for the trivial
extensions of $\mathbf{F}_{q}$.
