Results concerning chain conditions in rings or, more generally, modules give information about the lattice of ideals of the ring or submodules of the module. By considering modular lattices we can not only generalize theorems from Ring Theory but also prove results which can be applied to Grothendieck categories. We shall try to justify this approach by showing that it is natural and does give additional information not least because result automatically dualize. As one might expect generalizing results to modular lattices presents difficulties and we shall illustrate some of these.