An uncoupled Ore algebra is an abstraction of common properties of
linear partial differential, shift and q-shift operators.
Using uncoupled Ore algebras, we present an algorithm for finding
hyperexponential solutions of a system of linear differential,
shift and $q$-shift operators, or any mixture thereof, whose solution space is
finite-dimensional. The algorithm is applicable to
factoring modules over an uncoupled Ore algebra when the modules
are also finite-dimensional vector spaces over the field of