  It will be shown that if $\phi$ is a quasiperiodic flow on the $n$-torus that
is algebraic, if $\psi$ is a flow on the $n$-torus that is smoothly conjugate
to a flow generated by a constant vector field, and if $\phi$ is smoothly
semiconjugate to $\psi$, then $\psi$ is a quasiperiodic flow that is algebraic,
and the multiplier group of $\psi$ is a finite index subgroup of the multiplier
group of $\phi$. This will partially establish a conjecture that asserts that a
quasiperiodic flow on the $n$-torus is algebraic if and only if its multiplier
group is a finite index subgroup of the group of units of the ring of integers
in a real algebraic number field of degree $n$.
