Let R be an arbitrary ring with identity and M, a right R-module with Z 2 (M) the second
singular submodule of M. We call an endomrphism φ of M, a t-automorphism if φ ̄: M∕ Z 2 …

Let M and N be two modules. M is called automorphism N-invariant if for any essential
submodule A of N, any essential monomorphism f: A→ M can be extended to some g∈ Hom …

A module M is called an automorphism-invariant module if every isomorphism between two
essential submodules of M extends to an automorphism of M. This paper introduces the …

A module is defined to be an automorphism-invariant module if it is invariant under
automorphisms of its injective hull. Quasi-injective modules and, more generally, pseudo …

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 …

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 …

In this paper, we give some results of endomorphism rings of automorphism-invariant
modules. It shows that if M is an automorphisminvariant self-generator module with finite …

In this paper we study modules coinvariant under automorphisms of their projective covers.
We first provide an alternative, and in fact, a more succinct and conceptual proof for the …

A module M is called dual automorphism invariant if whenever X 1 and X 2 are small
submodules of M, then each epimorphism f: M/X 1→ M/X 2 lifts to an endomorphism g of M …

A module M is called automorphism-invariant if it is invariant under automorphisms of its
injective envelope. In this paper, we study the endomorphism rings of automorphism …