Rings of Morita contexts which are maximal orders

Let T = (R W V S) be a ring of Morita context which is a prime Goldie ring with its quotient ring (Q(R) Q(W) Q(V) Q(S)). We define the notion of an (R, S)-maximal module in Q(V) and that of an (S, R)-maximal module in Q(W) from order theoretical point of view and give some necessary and sufficient conditions for T to be a maximal order in terms of (R, S)-module V and (S, R)-module W. In case T is a maximal order, we explicitly describe the structure of v-T-ideals. These results are applied to obtain necessary and sufficient conditions for T to be an Asano order or a Dedekind order.