Strongly Goldie Extending Modules

Abstract

A submodule N of a right R-module M is said to be strongly large in case for any ,  with  , there exists an  such that  and . In this paper, we introduce strongly -extending modules which are particular -extending modules, and investigate their properties and characterizations. An R-module M is called strongly -extending if for each submodule X of M there exists a direct summand D of M such that  is strongly large in both X and D. Some sufficient conditions for a direct sum of strongly -extending modules to be strongly -extending are obtained. Examples to illustrate this concept are given.