On J–Lifting Modules

Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if for every submodule N of M, there exists a submodule K of N such that \mathop {\rm{K}}\limits^\prime \subseteq {\rm{M}}$?> M = K ⊕ K ′ ,   K ′ ⊆ M and N ∩ K ′ ≪ J K ′ . The am of this paper is to introduce properties of J–lifting modules. Especially, we give characterizations of J–lifting modules.We introduce J–coessential submodule as a generalization of coessential submodule . Finally, we give some conditions under which the quotient and direct sum of J–lifting modules is J–lifting.