System equivalence for AR-systems over rings

In this paper we introduce the notion of an AR-system over an arbitrary integral domain R. This type of systems can be used for the modeling of delay-differential systems with (in)commensurable delays. In this approach, the signal space is considered as a module M over R. We study system equivalence, and show that it is characterized by division properties of the system defining matrices over a ring R_M. R_M is a ring extension of R, explicitly depending on M. Finally, we apply these results to delay-differential systems.