Row reduced representations of behaviors over finite rings

Row reduced representations of behaviors over fields posses a number of useful properties. Perhaps the most important feature is the predictable degree property. This property allows a finite parametrization of the module generated by the rows of the row reduced matrix with prior computable bounds. In this paper we study row-reducedness of representations of behaviors over rings of the form Z_p r , where p is a prime number. Using a restricted calculus within Z_p r we derive a meaningful and computable notion of row-reducedness.