The composition of dualities in a nondegenerate Morita context (Q1295646)

Given an arbitrary Morita context \((R,{_RM_S},{_SN_R},S)\), the order-reversing maps between the lattices of submodules of \(_RM\), \(N_R\) and \(S_S\) are investigated. Several Galois connections, dualities (order-reversing bijections) and projectivities (order-preserving bijections) are considered under weak conditions on the context. When the Morita context is not degenerate, the preceding conditions hold and a nice diagram relates all the bijections among the lattices of submodules.