Generalizations of semicoprime preradicals

This article introduces the notions quasi-co-$n$-absorbing preradicals and semi-co-$n$-absorbing preradicals, generalizing the concept of semicoprime preradicals. We study the concepts quasi-co-$n$-absorbing submodules and semi-co-$n$-absorbing submodules and their relations with quasi-co-$n$-absorbing preradicals and semi-co-$n$-absorbing preradicals using the lattice structure of preradicals.