Sublattices of the Lattice of Pre-natural Classes of Modules

A pre-natural class of modules over a ring R is one that is closed under isomorphic copies, submodules, arbitrary direct sums, and certain essential extensions. The set pr(R) of all pre-natural classes is a lattice, which contains many previously studied lattices of R-module classes. The sublattice structure of pr(R) is studied in this paper and is related to ring and module properties of R