A module is called nilpotent-invariant if it is invariant under any nilpotent endomorphism of
its injective envelope [MT Koşan and TC Quynh, Nilpotent-invaraint modules and rings …

We introduce the notion of a t-nilpotent endomorphism of modules and study the modules
which are invariant under t-nilpotent endomorphisms of their injective envelope, such as …

Automorphism-invariant modules, due to Lee and Zhou, generalize the notion of quasi-
injective modules. A module which is invariant under automorphisms of its injective hull is …

A special type of injective module which is introduced by Ming is called p-injective if for
every a∈ R, every R-linear map from aR to M can be extended to a linear map from R to M …

We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …

Throughout this paper R will denote a ring with idenity element and M a unitary right module
over R. An R-module M is said to be direct injective if and only if given direct summand N of …

For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum
of injective right R-modules is injective, and R is right Noetherian if and only if every …

Let R be a ring. A right R-module M is called minimal quasi-injective if every homomorphism
from a simple submodule of M to M can be extended to an endomorphism of M. Some …

We first prove that if a monomorphism is a phantom envelope of a left R-module, then its
cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an Ext Ext …

A theorem due to Warfield states that “a ring R is left serial if and only if every (finitely
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …