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

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 …

The notion of⊕-supplemented modules is a proper generalization of lifting modules. As a
proper generalization of⊕-supplemented modules, we introduce (D 12)-modules and obtain …

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 …

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 paper, we study a module which is lifting and supplemented relative to a module
class. Let R be a ring, and let X be a class of R-modules. We will define X-lifting modules …

Harada (cf.) introduced the lifting property for maximal submodules and the extending
property for simple submodules, and Oshiro (cf.) definitely introduced lifting modules and …

Finitely-hollow lifting and hollow-weak lifting modules are two generalizations of hollow
lifting module which is a weaker version of lifting module. In this paper, we have defined …

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 …