On some operations in the lattice of submodules determined by preradicals

In the lattice $\boldsymbol L(_RM)$ of all submodules of a module $_RM$ four operations are defined using the standard preradicals: $\alpha$-product, $\omega$-product, $\alpha$-coproduct and $\omega$-coproduct. Some properties of these operations, as well as some connections with the lattice operations of $\boldsymbol L(_RM)$ are indicated. For characteristic submodules these operations were studied in the work [5].