Rings of Morita contexts which are maximal orders

Abstract

Let [Formula: see text] be a ring of Morita context which is a prime Goldie ring with its quotient ring [Formula: see text]. We define the notion of an [Formula: see text]-maximal module in [Formula: see text] and that of an [Formula: see text]-maximal module in [Formula: see text] from order theoretical point of view and give some necessary and sufficient conditions for [Formula: see text] to be a maximal order in terms of [Formula: see text]-module [Formula: see text] and [Formula: see text]-module [Formula: see text]. In case [Formula: see text] is a maximal order, we explicitly describe the structure of [Formula: see text]-[Formula: see text]-ideals. These results are applied to obtain necessary and sufficient conditions for [Formula: see text] to be an Asano order or a Dedekind order.