Throughout this paper, R denotes an associative ring with identity, and all modules are unital right R-modules. Let N ≤ M mean N is a submodule of a module M . A submodule N of a module M is called small in M if, for every submodule K of M , the equality M = N + K implies M = K . A submodule P is a supplement of N in M if M = P + N and P ∩ N is small in P , while M is called supplemented if every submodule of M has a supplement in M . In [1], M is said to be principally supplemented if every cyclic submodule of M has a supplement in M . Also, a module M is called (principally ) lifting if, for every (cyclic) submodule N of M , there is a decomposition M = D ⊕ D′ such that D ⊆ N and D′ ∩ N is small in M .
