  We present a method for determining the one-dimensional submodules of a
Laurent-Ore module. The method is based on a correspondence between
hyperexponential solutions of associated systems and one-dimensional
submodules. The hyperexponential solutions are computed recursively by solving
a sequence of first-order ordinary matrix equations. As the recursion proceeds,
the matrix equations will have constant coefficients with respect to the
operators that have been considered.
