γ-small submodules and γ-lifting modules

In this paper we introduce a new generalization of small submodules, namely γ-small submodules. We call a submodule K of a module M, γ-small provided M = K + L with M/L noncosingular, implies M = L. Applying this concept, we define a generalization of lifting modules entitled γ-lifting modules and investigate their some general properties. It is proved that any supplement submodule of a γ-lifting module is γlifting.