In this paper, we provide the basic properties of (semi) simple hypermodules. We show that
if a hypermodule M is simple, then (E nd (M),·) is a group, where E nd (M) is the set of all …

Given a ring R, we define its right i-profile (resp. right p-profile) to be the collection of
injectivity domains (resp. projectivity domains) of its right R-modules. We study the lattice …

We approach the analysis of the extent of the projectivity of modules from a fresh perspective
as we introduce the notion of relative subprojectivity. A module M is said to be N …

Given modules M and N, M is said to be N-subinjective if for every extension K of N and
every homomorphism φ: N→ M there exists a homomorphism ϕ: K→ M such that ϕ| N= φ …

Given modules M and N, M is said to be N-subprojective if for every epimorphism g: B→ N
and homomorphism f: M→ N, there exists a homomorphism h: M→ B such that gh= f. For a …

In a recent paper of Alahmadi, Alkan and López-Permouth, a ring R is defined to have no
(simple) middle class if the injectivity domain of any (simple) R-module is the smallest or …

As a mean to provide intrinsic characterizations of poor modules, the notion of a pauper
module is introduced. A module is a pauper if it is poor and has no proper poor direct …

In this paper, poor abelian groups are characterized. It is proved that an abelian group is
poor if and only if its torsion part contains a direct summand isomorphic to⊕ p∈ P ℤ p …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …

An analog of the injective profile of a ring, with relative injectivity replaced by relative pure-
injectivity, is investigated. Emphasis is placed on comparing and contrasting the properties …