On Sub-Networks over Proper Ideals of Dynamical Networks over Finite Rings

This paper investigates dynamical networks over finite rings and their sub-networks over proper ideals. A necessary and sufficient condition, based on the semi-tensor product of matrices, to determine whether an ideal is a proper ideal is obtained. A new method for the construction of a sub-network over a proper ideal is also proposed. Finally, two examples are presented to demonstrate the proposed method's effectiveness.