An Approach to Goldie Extending Modules on the Class of Cyclic Submodules

In this article, we provide a class of modules that is comparable to -extending and -extending modules. We specify what a module M is as -extending if and only if for each cyclic submodule A of M, there exists a direct summand D of M such that A is essential in both A and D. We look into -extending modules and locate this inference between the other extending properties. We present some of characterizations of -extending condition. We show that the direct sum of -extending need not be -extending and deal with decompositions for -extending concept."