Abstract. A rectangular Ore algebra is a common abstraction of properties of rings of linear (partial) differential or shift operators proposed recently by G. Labahn and Z. Li. Under this setting, we interpret the reducibility and decomposability of systems of linear differential and linear difference equations with finite-dimensional solution space in terms of D-module theory. This interpretation enables us to generalize Beke's factorization algorithm and the eigenring decomposition algorithm to factor or decompose theoretically systems in a unified way.