One theorem of Cohn

Let $F$ be the field of algebraic functions of one variable over the field of constants $k$, $v$ be a point of field $F/k$, and $A_v$ be the ring of functions not having poles outside point $v$. It is proved that $A_v$ is a $GE_2$-ring if and only if it coincides with the ring $k[x]$ of polynomials of one variable over field $k$.