Lifting modules plays important roles in module theory. H-supplemented modules are a nice
generalization of lifting modules which have been studied extensively recently. In this article …

The class of $ H $-supplemented modules, which is a nice generalization of that of lifting
modules, has been studied extensively in the last decade. As the concept of …

A module M is said to be H-supplemented if, for any submodule X of M, there exists a direct
summand M′ of M such that M= X+ Y if and only if M= M′+ Y for all Y⊆ M (cf.[SH …

⊕-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 …

Let M be a module over a ring R. We call M, γ γ-H-supplemented provided for every
submodule N of M there is a direct summand D of M such that M= N+ XM= N+ X if and only if …

Let τM be any preradical for σM and N any module in σM. A module N is called τM-lifting if
for every submodule K of N, there is a decomposition K= A⊕ B, such that A is a direct …

A module M is called H-supplemented if for every submodule A of M there is a direct
summand A′ of M such that A+ X= M holds if and only if A′+ X= M for each submodule X …

In this paper, we study modules with the property that every exact fully invariant submodule
has a complement which is a direct summand. This new class of modules properly contains …

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 …

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 …