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 …

Given modules RM and AR, RM is said to be absolutely AR-pure if A⊗ M→ A⊗ B is a
monomorphism for every extension RB of RM. For a module AR, the absolutely pure domain …

In a recent paper, Holston et al. have defined a module M to be N-subprojective if for every
epimorphism g: B→ N and homomorphism f: M→ N, there exists a homomorphism h: M→ B …

This work aims to contribute to the study of rings in terms of their simple modules. Vast
research has been done in this direction to investigate rings whose simple modules are all …

Two obvious classes of quasi-injective modules are those of semisimples and injectives. In
this paper, we study rings with no quasi-injective modules other than semisimples and …

The aim of this paper is to present new results and generalize some results about indigent
modules. The commutative rings whose simple modules are indigent or injective are fully …

While mutual congeniality of bases is known to guarantee that basic modules from so-
related bases are isomorphic, the question of what can be said about isomorphism of basic …

A pure-injective module M is said to be pi-indigent if its subinjectivity domain is smallest
possible, namely, consisting of exactly the absolutely pure modules. A module M is called …

We further the study of rings with no middle class by focusing on an interpretation of that
property in terms of the lattice of hereditary pretorsion classes over a given ring. For non …

Proper classes (or exact structures) offer rich research topics due to their important role in
category theory. Motivated by the studies on opposite of injective modules, we introduce a …