Warfield proved that every injective module has the exchange property. This was
generalized by Fuchs who showed that quasi-injective modules satisfy the exchange …

Automorphism-invariant modules Page 30 Contemporary Mathematics Volume 634 , 2015
http://dx. doi. org/10.1090/conm/634/12688 Automorphism-Invariant Modules Pedro A. Guil …

A module M is called a D 4-module if, whenever A and B are submodules of M with M= A⊕
B and f: A→ B is a homomorphism with Im f⊆⊕ B, we have ker f⊆⊕ A. The class of D 4 …

In this paper we develop a general theory of modules which are invariant under
automorphisms of their covers and envelopes. When applied to specific cases like injective …

An R-module M is called a C 4-module if, whenever A 1 and A 2 are submodules of M with
M= A 1⊕ A 2 and f: A 1→ A 2 is an R-homomorphism with ker f⊆⊕ A 1, we have I mf⊆⊕ A …

We use the type theory for rings of operators due to Kaplansky to describe the structure of
modules that are invariant under automorphisms of their injective envelopes. Also, we …

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 …

In this paper we study the Schröder–Bernstein problem for modules. We obtain a positive
solution for the Schröder–Bernstein problem for modules invariant under endomorphisms of …

In this paper, we study rings having the property that every right ideal is automorphism-
invariant. Such rings are called right a-rings. It is shown that (1) a right a-ring is a direct sum …

Rings in which each finitely generated right ideal is automorphism-invariant (right fa-rings)
are shown to be isomorphic to a formal matrix ring. Among other results it is also shown that …