For the recently defined notion of strongly lifting modules, it has been shown that a direct
sum is not, in general, strongly lifting. In this paper we investigate the question: When are the …

In this note, we investigate the relationship between almost projective modules and
generalized projective modules. These concepts are useful for the study on the finite direct …

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

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 over a ring R is called hollow-lifting if every submodule N of M with M/N hollow
contains a direct summand K of M such that N/K is a small submodule of M/K. It is known that …

The notions of t-lifting modules and t-small submodules of a module M were introduced in
Amouzegar et al.(Vietnam J. Math. 42, 159–169, 2014). But the authors restricted the …

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 is said to be H-supplemented if, for any submodule X of M, there exists a direct
summand M′ of M such that M= X+ Y if and only if M= M′+ Y for all Y⊆ M (cf.[SH …

Let R be a ring and M a right R-module. M is called a cofinitely lifting module if for any
cofinite submodule N of M, there exists a direct summand K of M such that K≤ N and N/K≪ …

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 …