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We define a module  M  to be-extending if for each exact submodule  X  of  M  there exists a direct summand  D  of  M  such thatis essential in both  X  and  D . We investigate-extending modules and locate the implications between the other extending properties. We study decomposition theory and extensions for-extending concept. We show that if a ring is right-extending, then so its essential overring. It is shown that-extending property is inherited by its rational hull. We provide examples by making special choices of left exact preradicals.

Goldie extending property on the class of exact submodules