Entwined structures (A,C, ψ) were introduced by Brzeziński and Majid to study the interdependence of an R-algebra A and an R-coalgebra C, R a commutative ring. It turned out that this relationship can also be expressed by the fact that A⊗R C has a canonical A-coring structure. More generally weak entwined structures and their modules were studied by Caenepeel and Groot and it was suggested by C...