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 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 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 said to be lifting if, for any submodule X of M, there exists a decomposition M=
A⊕ B such that A⊆ X and X/A is a small submodule of M/A. A lifting module is defined as a …

المعممة - مقاسات الرفع المجوفه Generalized-hollow lifting modules Page 1 Hasan Iraqi Journal
of Science, 2016, Vol. 57, No.3B, pp:2089-2093 _______________________________ *Email …

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 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 …

We give necessary and sufficient conditions for a module M with a decomposition that
complements maximal direct summands to be a lifting module. We apply our results to get a …

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 …