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

Throughout this paper R is a ring with identity and every i?-module is unital. Let r be a
hereditary torsion theory with respect to R (see Golan [3]). A submodule N of a right i …

In [2 1, Fuchs has shown that R is a test module for quasiinjective modules. He showed that
if M is a right R-module, M is quasi-injective if and only if for each right ideal K of R, every R …

An R-module M is said to be quasi-injective if every R-homomorphism a: S+ M, S a
submodule of M, is induced by an R-endomorphism of M. A well known result of Johnson …

Using U-torsionless module we characterize U-neat submodules and Au-injective modules.
If M is a left R-module, U is E (M)-injective and Eu (M)/M does not contain a nonzero …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …

Let R be a ring with identity element and M be a unitary left R-module. M is called quasi-
injective if every element in Hom^ Af, M) for any R-module N in M is extened to an element in …

1. Let R be a ring with identity not equal to zero. A right R-module is said to be quasi-
injective (pseudo-injective) if for every submodule N of M, every R-homomorphism (R …

Classically, the Auslander–Bridger transpose finds its best applications in the well-known
setting of finitely presented modules over a semiperfect ring. We introduce a class of …

Let $ _RM $ be a left $ R $-module such that ${\operatorname {Hom} _R}(M, U)\ne 0$ for
any nonzero submodule $ U $ of $ M $, let $ E (M) $ denote the injective hull of $ M $, and …