Autonomy properties of multidimensional linear systems over rings

Based on the notions of rank and reduced rank from commutative algebra, we discuss several aspects of the concept of autonomy for multidimensional discrete linear systems over finite rings of the form Z/mZ. We review several algebraic characterizations of autonomy that are equivalent for systems over fields and investigate their relationship in the ring case. The strongest of these notions turns out to be equivalent to the non-existence of trajectories with finite support (besides the zero trajectory), and the weakest one amounts to the fact that the system has no free variables (inputs).