A Recursive Method for Determining the One-Dimensional Submodules of   Laurent-Ore Modules
  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. 
Ziming Li, Michael F. Singer, Min Wu, Dabin Zheng