A ring R is said to be left pure-hereditary (resp. RD-hereditary) if every left ideal of R is pure-
projective (resp. RD-projective). In this paper, some properties and examples of these rings …

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

We study direct-sum decompositions of RD-projective modules. In particular, we investigate
the rings over which every RD-projective right module is a direct sum of cyclically presented …

In a recent paper, Mao has studied min-pure injective modules to investigate the existence
of min-injective covers. A min-pure injective module is one that is injective relative only to …

A famous theorem of algebra due to Osofsky states that “if every cyclic left R-module is
injective, then R is semisimple”. Therefore, a natural question of this sort is:“What is the class …

A module KR is said to be RL-subflat if for every short exact sequence 0→ U→ D→ L→ 0 of
left R-modules, the sequence 0→ K⊗ U→ K⊗ D→ K⊗ L→ 0 is exact. The subflat domains of …

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 …

Abstract Given modules $ A_ {R} $ and $ _ {R} B $, $ _ {R} B $ is called absolutely $ A_ {R}
$-pure if for every extension $ _ {R} C $ of $ _ {R} B $, $ A\otimes B\rightarrow A\otimes C …

A left R-module M is said to be left singly injective if Ext R 1 (F/K, M)= 0 for any cyclic
submodule K of any finitely generated free left R-module F. In this paper, we study the notion …

The subjectivity domain of a module allows us to evaluate how close (or far) a module is
from being injective. In this paper, we consider three families of rings characterized by their …