On some operations in the lattice of submodules determined by preradicals. (Q2883525)

For a given module, four products are defined in the lattice of its submodules. These are extensions of the \(\alpha\)-product and the \(\omega\)-product which have been defined earlier for characteristic submodules. By replacing the product of preradicals with its coproduct, two dual products are obtained namely the \(\alpha\)-coproduct and the \(\omega\)-coproduct. The \(\alpha\)-product has been studied earlier in connection with prime modules and the \(\omega\)-coproduct in the study of coprime modules.NEWLINENEWLINE Various properties of these products are investigated; in particular also their behaviour with respect to the lattice operations in the lattice of all submodules.