On Large-Small submodule and Large-Hollow module

Abstract

Abstract The goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤ e M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.

Topics & Concepts