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-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 …

The study of pure-projectivity is accessed from an alternative point of view. Given modules M
and N, M is said to be N-pure-subprojective if for every pure epimorphism g: B → N g: B→ N …

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 …

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 …

The study of pure-injectivity is accessed from an alternative point of view. A module M is
called pure-subinjective relative to a module N if for every pure extension K of N, every …

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 …

In this paper, we investigate modules whose elements of their injectivity domains satisfy the
fixed property p. In particular, quasi-poor modules as a generalization of poor modules are …

A p-indigent module is one that is subprojective only to projective modules. An RD-
projective module is subprojective to any torsionfree (and flat) module. An RD-projective …