abstract
- For L and N fully invariant submodules of an R-module M, the internal coproduct is defined in preradical terms as: (Formula presented.). We define the concept of coidempotent submodule and obtain a new characterization of the semisimple rings. The concepts of coprime and semicoprime submodules (ideals) are defined. We study the properties of these modules and obtain results for Kasch modules (left Kasch rings). Finally, we give a topology to the set of coprime submodules of an R-module M and provide a characterization when this topology is (Formula presented.) (Fréchet). © 2025 Taylor & Francis Group, LLC.