Pole shifting for families of systems: The dimension one case

We prove that ifR is a one-dimensional ring, then each basic submodule of a freeR-moduleE contains a rank one projective summand ofE. As it is known that this property implies the pole assignability property for rings, it follows that any one-dimensional ring has the pole assignability property. Applications to systems over rings are briefly explained. The authors were partially supported by NSF grants.