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 is an element of M, s is an element of R with ms not equal 0 there exists an r is an element of R such that mr is an element of N and mrs not equal 0. In this note, we also define and study strongly large closed submodules and strongly large complement submodules.