" The study of modules which are invariant under the action of certain subsets of the
endomorphism ring of their injective envelope can be drawn back to the pioneering work of …

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 study the modules that are coinvariant under the idempotent endomorphisms of their
covers. Some generalizations of discrete and continuous modules are introduced and …

A module M is called pseudo-projective if every epimorphism from M to each quotient
module of M can be lifted to an endomorphism of M. In this paper, we study some properties …

A right R-module N is called pseudo semisimple-M-injective if for any monomorphism from
every semisimple submodule of M to N, can be extended to a homomorphism from M to N. In …

A module M over a ring R is called automorphism-invariant if M is invariant under
automorphisms of its injective hull E (M) and M is called co-Hopfian if each injective …

In this paper, we give some results of indecomposable rings in which finitely generated right
ideals are automorphism-invariant. They are called fa-rings. It shows that any …

A ring is called a right $ a $-ring if every right ideal is automorphism invariant. We describe
some properties of $ a $-rings over semiperfect rings. It is shown that an I-finite right $ a …

A module M is said to be an automorphism liftable module iffor each submodule N of M,
every automorphism of the quotient M= N canbe lifted to an endomorphism of M. In this work …

This paper is a review of results on endomorphism-extendable modules, automorphism-
extendable modules,-injective modules, endomorphism-liftable modules, and automorphism …