We introduce the notion of I-lifting modules as a proper generalization of the notion of lifting
modules and present some properties of this class of modules. It is shown that if M is an I …

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 …

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 …

Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if
for every submodule N of M, there exists a submodule K of N such that ${\rm {M}}={\rm …

⊕-supplemented modules as a famous generalization of lifting (projective supplemented)
modules were widely studied in the last decades. In this paper, we peruse a homological …

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 notions of t-lifting modules and t-dual Baer modules, which are
generalizations of lifting modules. It is shown that an amply supplemented module M is t …

Following (Kosa̧n in Algebra Colloq. 14: 53–60, 2007), a module M is called δ-
supplemented if, for every submodule of N of M, there exists L≤ N such that M= N+ L and …

Endo-permutation modules arise in a number of ways in the representation theory of® nite
groups, in particular in connection with equivalences between blocks and as sources of …

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 …