In this paper, we study the behavior of endomorphism rings of indecomposable (uniform)
quasi-injective modules. A very natural question here is, for a morphism f: A→ B, with A, B …

We show that the endomorphism rings of kernels ker ϕ of non-injective morphisms ϕ
between indecomposable injective modules are either local or have two maximal ideals, the …

In this paper we prove that a module M is invariant under automorphisms of its X-envelope if
and only if M is invariant under monomorphisms of its X-envelope where X is an enveloping …

Let R be a ring and ℒ a class of R-modules. An R-module N is called ℒ-injective if for all L∈
ℒ. An ℒ-injective hull of an R-module M is defined to be a homomorphism φ: M→ F with F ℒ …

In this paper certain injectivity conditions in terms of extensions of monomorphisms are
considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if …

An R-module M is called principally quasi-injective if each R-hornomorphism from a
principal submodule of M to M can be extended to an endomorphism of M. Many properties …

This paper contains new and known results on homomorphisms that are close to regular.
The main results are presented with proofs. All rings are assumed to be associative and with …

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 …

Let u be an idempotent kernel functor on a commutative noetherian ring R and T be the
topology on R associated with a. The problem of decomposing the o-injective hull of a …

Self-injective and PF endomorphism rings Page 1 ISRAEL JOURNAL OF MATHEMATICS, Vol.
58, No. 3, 1987 SELF-INJECTIVE AND PF ENDOMORPHISM RINGS BY JL GARCiA …