Modules for which every noncosingular submodule is a summand

A module M is lifting if and only if M is amply supple- mented and every coclosed submodule of M is a direct summand. In this paper, we are interested in a generalization of lifting modules by re- moving the condition amply supplemented and just focus on modules such that every non-cosingular submodule of them is a summand. We call these modules NS.We investigate some general properties of NS-modules. Several examples are provided to separate different concepts. It is shown that every non-cosingular NS-module is a direct sum of indecomposable modules. We also discuss on nite direct sums of NS-modules.