on c-extending modules

Let w be a unitary left a-module, where a is an arbitrary ring with identity. in this note, we introduce a new generalization of essential submodules, namely the c-essential submodule. a submodule n of a module w is called c-essential if every submodule which properly contains n is essential in w. we use this concept to investigate a new generalization of extending modules. a module w is called a c-extending module, if every submodule is c-essential in a direct summand of w. some interesting results regarding c-essential submodules and c-extending modules are obtained in this paper.