Proper classes (or exact structures) offer rich research topics due to their important role in
category theory. Motivated by the studies on opposite of injective modules, we introduce a …

For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

Let R be a ring with identity. Given a positive integer n, a unitary right R-module X is called n–
injective provided, for every n-generated right ideal A of R, every R-homomorphism φ: A→ X …

In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

Let R be a left artinian ring such that every finitely presented right. ft-module is of finite
endolength. It is shown that the cardinality of the set of isomorphism classes of preinjective …

Abstract A right R–module E over a ring R is said to be maximally injective in case for any
maximal right ideal m of R, every R–homomorphism f: m→ E can be extended to an R …

The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …

We prove the following results for a ring R.(a) If C is a class of right R-modules closed under
direct summands and isomorphisms, then every right R-module has an epic C-envelope if …

A ring R is called a V-ring, respectively SSI-ring, respectively QII-ring if simple, respectively
semisimple, respectively quasi-injective, right R-modules are injective. We show that R is …

If R is a right non-singular ring (with 1) and Q is its (RE Johnson) maximal right quotient ring,
then the R-epimorphism∑ ipi⊗ qi→∑ piqi from (Q⊗ RQ) R to QR is not in general a …