Strongly large module extensions

Abstract

In this paper, we introduce strongly large submodules and investigate their properties. A submodule N of a right R-module M is said to be strongly large in case for any m ∈ M, s ∈ R with ms≠ 0 there exists an r ∈ R such that mr ∈ N and mrs≠ 0. In this note, we also define and study strongly large closed submodules and strongly large complement submodules.