One of the main results of this paper is the characterization of left FP-injective rings as rings
over which every finitely presented right module is torsionless. The necessity of the …

A ring is quasi-Frobenius if and only if every injective right R-module is projective. Thus, the
ring has the property that each right-module embeds in a free module if and only if the ring is …

An R-module M is called weakly co-Hopfian if any injective endomorphism of M is essential.
The class of weakly co-Hopfian modules lies properly between the class of co-Hopfian and …

We carry out an extensive study of modules MR with the property that M/f (M) is singular for
all injective endomorphisms f of M. Such modules called “quasi co-Hopfian”, generalize co …

In this article, FP-injective complexes are introduced and studied. We prove that (⊥ ℱℐ, ℱℐ)
is a hereditary cotorsion theory if and only if R is a left coherent ring, where ℱℐ denotes the …

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 …

We characterize right Noetherian rings over which all simple modules are almost injective. It
is proved that R is such a ring, if and only if, the complements of semisimple submodules of …

(right) PF-rings. This class of rings and another related generalization of quasi-Frobenius
rings, the (two-sided) cogenerator rings, have been studied recently by a number of authors …

We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …