Quasi-$n$-absorbing and semi-$n$-absorbing preradicals

Abstract

The aim of this paper is to introduce the notions of quasi-$n$-absorbing preradicals and of semi-$n$-absorbing preradicals. These notions are inspired by applying the concept of $n$-absorbing preradicals to semiprime preradicals. Also, we study the concepts of quasi-$n$-absorbing submodules and of semi-$n$-absorbing submodules and their relations with quasi-$n$-absorbing preradicals and semi-$n$-absorbing preradicals.