A generalization of goldie extending modules via ec-closed submodules

In this article, we introduce a class of modules which is analogous to that of -extending and -extending modules. We define a module M to be -extending if and only if for each ec-closed submodule A of M, there exists a direct summand D of M such that A is essential in both A and D. We investigate -extending modules and locate the implications 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.