Abstract
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 when R–tors and R–nat are isomorphic, only studying the structure of as an idiom, and its frame of nucleus.
Acknowledgment
The author wish to express his gratitude to the referee for his valuable remarks and suggestions.