A module M is called lifting if every submodule N of M, contains a direct summand K of M
such that N/K≪ M/K. We call a module M cf-lifting if every coessentialy a finitely generated …

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 $ is lifting if and only if $ M $ is amply supplemented and‎‎ every coclosed
submodule of $ M $ is a direct summand‎.‎ In this paper‎,‎ we are‎‎ interested in a generalization …

A module M is called hollow-lifting if every submodule N of M such that M/N is hollow
contains a direct summand D\subseteq N such that N/D is a small submodule of M/D. 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 …

In this paper, we introduce and study the concept of FI-hollow-lifting modules which is a
proper generalization of hollow-lifting modules. We say M called a fully invariant hollow …

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 …

In this note, we introduce the (small, pseudo-) ℬ (M, X)-cojective modules and we generalize
(small, pseudo-) cojective modules via the class ℬ (M, X). Let M= M1⊕ M2 be an X-amply …

Abstract In 1984, Oshiro [11] has studied the decomposition of continuous lifting modules.
He obtained the following: every continuous lifting module has an indecomposable …

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 …