On natural sets on an idiom

We introduce and develop the concept of natural set for an idiom (complete upper-continuous modular lattice), which is the analogous of the well-known natural classes of modules. For these natural sets, we generalize important results of the natural classes of modules, and get relevant information about the idiom. In particular, we characterize when the frame of nucleus on an idiom is Boolean. We also apply these results to classes of modules, proving whenR-torsandR-natare isomorphic, only studying the structure ofas an idiom, and its frame of nucleus.