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 …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

1. Throughout this paper all rings will have an identity and all modules will be unitary. Given
three non-zero left ideals I, J and L in a simple left Noetherian hereditary domain R, then a …

The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …

Let ℒ be a class of right R-modules. The notions of ℒ-injectivity and ℒ-flatness are used to
investigate right ℒ-Noetherian rings, right ℒ-hereditary rings, and right ℒ-coherent rings. For …

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 …

ABSTRACT A module M is called strongly FP-injective if Ext i (P, M)= 0 for any finitely
presented module P and all i≥ 1.(Pre) envelopes and (pre) covers by strongly FP-injective …

This note discusses the structure of a ring R with the ascending chain condition (= acc) on
annihilator left ideals having the property that each module homomorphism from a principal …

Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-
injective if Ext d+ 1 R (P, M)= 0 for any n-presented R-module P. M is said to be (n, d) …

A left FPF ring is a ring R such that every finitely generated faithful left R-module generates
the category of left R-modules. It is shown that such rings split into R= A⊕ B, where A is a …