Submersive Rational Difference Systems and Formal Accessibility

Abstract. We show that a rational difference system corresponds to a proper, prime and reflexive (difference) ideal iff the system is submersive, which can be verified by computing the rank of a matrix. An explicit construction is described for the inversive closure of the difference field associated with a proper, prime and reflexive ideal. Over this closure, a purely algebraic setting is presented for applying computer algebra techniques to a pseudo-linear algebra approach for nonlinear control systems. 1