The composition of dualities in a nondegenerate Morita context Original Research Article

The relations between the lattices of submodules of members of an Morita context are studied. The pairs of reversing order maps are defined, which determine the dualities between the sets of ‘closed’ submodules. In the rather weak conditions these dualities can be composed obtaining the projectivities defined by simple maps. If the context is nondegenerate then the square is shown consisting of four dualities and two projectivities co-ordinated between them.