Goldie Supplement Extending Modules

In this paper, we call the module N the Goldie supplement extending module (GSCS-module) which is a new generalization weaker than the Goldie extending module and stronger than the Goldie weakly supplement extending module. We discuss the relation between Goldie supplement extending module and other notions such as the Goldie extending module and the supplement extending module. Moreover, we explain when the submodule of Goldie supplement extending is a Goldie supplement extending module. Furthermore, we show that the direct sum of GSCS-module holds only under certain conditions.