Loewy and primary decompositions of D-modules

Two kinds of decompositions of a D-module are introduced in this article, a Loewy-decomposition and a primary decomposition. Algorithms are described which allow to construct decompositions for finite-dimensional D-modules. Both decompositions rely on the concept of the D-module of relative syzygies introduced in the paper. Furthermore an algorithm is described which tests whether two given D-modules are isomorphic under the relevant type of transformations.