Generalized-hollow lifting modules

Let R be any ring with identity, and let M be a unitary left R-module. A submodule K of M is called generalized coessential submodule of N in M, if N/K⊆ Rad(M/K). A module M is called generalized hollow-lifting module, if every submodule N of M with M/N is a hollow module, has a generalized coessential submodule of N in M that is a direct summand of M. In this paper, we study some properties of this type of modules.