Preradicals and characteristic submodules: connections and operations

Abstract

For an arbitrary module M∈R-Mod the relation between the lattice Lch(RM) of characteristic (fully invariant) submodules of M and big lattice R-pr of preradicals of R-Mod is studied. Some isomorphic images of Lch(RM) in R-pr are constructed. Using the product and coproduct in R-pr four operations in the lattice Lch(RM) are defined. Some properties of these operations are shown and their relations with the lattice operations in Lch(RM) are investigated. As application the case RM=RR is mentioned, when Lch(RR) is the lattice of two-sided ideals of ring R.