In this paper we introduce the (∗)-generalized projective modules as a proper
generalization of projective modules. We also investigate the” When is direct sum of two …

In this note, we investigate the relationship between almost projective modules and
generalized projective modules. These concepts are useful for the study on the finite direct …

In this study, it is investigated the relation between almost projective modules and
generalized projective modules. These concepts are useful for the study on finite direct sum …

For the recently defined notion of strongly lifting modules, it has been shown that a direct
sum is not, in general, strongly lifting. In this paper we investigate the question: When are the …

Using the class δ of all singular R-modules, we introduce and characterize δ-lifting modules,
δ-supplements and δ-coclosed submodules, and give some equivalent conditions to …

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 purpose of this paper is to further study the concept of a very important module theory
namely principally supplemented modules. Therefore, our work presents some properties of …

In this paper we introduce the concept of lifting modules with respect to a submodule. Let M
be a module and U≤ M. We call M, U-lifting if for every submodule N of M there exists a …

(N) π1=(N+ M2) π1=((N+ M2)∩(M1+ M2)) π1=(((N+ M2)∩ M1)+ M2) π1=((N+ M2)∩ M1)
π1=(N+ M2)∩ M1 and so (N) π1= M1 if and only if M1⊆ N+ M2, that is, N+ M2= M. Finally, if …

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 …