Let $ R $ be any ring and let $ M $ be any right $ R $-module. $ M $ is called hollow-lifting if
every submodule $ N $ of $ M $ such that $ M/N $ is hollow has a coessential submodule …

A module M over a ring R is called a lifting module if every submodule A of M contains a
direct summand K of M such that A/K is a small submodule of M/K (eg, local modules are …

Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules
Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for …

A module M is called extending if, for any submodule X of M, there exists a direct summand
of M which contains X as an essential submodule, that is, for any submodule X of M, there …

Keskin and Harmanci defined the family B (M, X)= ${A {\leq} M|{\exists} Y {\leq} X,{\exists} f
{\in} Hom_R (M, X/Y),\; Ker\; f/A {\ll} M/A} $. And Orhan and Keskin generalized projective …

Discrete (quasi-discrete) modules form an important class in module theory, they are studied
extensively by many authors. The class of lifting modules is obtained by considering only …

A module M is lifting if for every submodule A of M, there exists a direct summand B of M
such that B≤ A and A/B small in M/B. Every non-cosingular lifting module has the summand …

We say that a module M is weak lifting if M is supplemented and every supplement
submodule of M is a direct summand. The module M is called lifting, if it is weak lifting and …

The class of $ H $-supplemented modules, which is a nice generalization of that of lifting
modules, has been studied extensively in the last decade. As the concept of …

A module M is called generalized extending if for any submodule N of M, there is a direct
summand K of M such that N≤ K and K/N is singular. Any extending module and any …