… of a quasi-injective module is quasi-injective, we have the corollary from Proposition 1.5. If we
consider R as a left R-module, … a quasi-injective module M and its injective envelope E(M). …

… M is a nonzero quasi-injective module. It is known … ϋί-modules. Harada has shown that for
left Noetherian rings M = Σ 0 Ma where the ikfα's are indecomposable quasi-injective modules …

… principally injective rings and quasi-injective modules are extended to these modulej. As
one application, we show that, for a finite-dimensional quasi-injective module M in which every …

… It is known (Harada [5]) that a direct sum of finitely many copies of a quasi-injective
module is quasi-injective. We show that if a direct sum of two copies of a pseudo-injective …

… , respectively semisimple, respectively quasi-injective, right Ä-modules are injective. We show
that … The rings R which have the property that quasi-injective right Rmodules are injective (…

… The main purpose of this paper is to extend some results on completely reducible modules
to quasi-injective modules by replacing “irreducible submodules” with “uniform submodules”. …

… R-module with S = End(MR). The module M is called almost principally quasi-injective (or …
The module M is called almost principally quasi-injective (briefly, APQ-injective) if, for any m …

… quasi-injective modules to nonsingular injective modules. Applications include the uniqueness
of nth roots: If A and B are quasi-injective modules … , all modules are unital right modules, …

… (1) Every quasi-injective module is (m, n)-quasi-injective for all positive integers m and n [2, …
(m, n)-quasi-injective. (3) MR is PQ-injective if and only if MR is (1, 1)-quasi-injective. (4) MR …

… for quasi-injective modules. Several conditions are given which imply that a quasi-injectixe
module is cancellative. Finally, we consider applications to compressible modules and rings …