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≪ …

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 …

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 …

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 …

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 …

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 …

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

A module M is called lifting if every submodule A of M contains a direct summand B of M
such that Bce,→ A in M. We call M is (strongly) FIlifting if every fully invariant submodule A of …

Lifting modules as a main concept in module theory have been studied and investigated
extensively in recent decades. The first author in [1] tried to consider and investigate this …

We introduce the concepts of lifting modules and (quasi‐) discrete modules relative to a
given left module. We also introduce the notion of SSRS‐modules. It is shown that (1) if M is …