  Suppose that $h$ and $g$ belong to the algebra $\B$ generated by the rational
functions and an entire function $f$ of finite order on ${\Bbb C}^n$ and that
$h/g$ has algebraic polar variety. We show that either $h/g\in\B$ or
$f=q_1e^p+q_2$, where $p$ is a polynomial and $q_1,q_2$ are rational functions.
In the latter case, $h/g$ belongs to the algebra generated by the rational
functions, $e^p$ and $e^{-p}$.
