Let R be a ring and M a right R-module. Let σ [M] be the full subcategory of Mod-R
subgenerated by M. An M-natural class 𝒦 is a subclass of σ [M] closed under submodules …

Throughout, all rings R are associative with identity, and all inodules are unitary right R-
modules. By a class K of modules we inean K is a collection of nlodules such that K is closed …

A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

A saturated class Δ of modules is any class of nonsingular right 7?-modules closed under
direct sums, injective hulls, submodules and isomorphic copies. Saturated classes are used …

Throughout R will represent a ring with unit element 1, and all modules will be unitary 7?-
modules. We call a module M a completely indecomposable module if the endomorphism …

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 …

Let ${R_0} $ be a skew field, or more generally, a finite product of full matrix rings over skew
fields. Let ${({R_\lambda}) _ {\lambda\in\Lambda}} $ be a family of faithful ${R_0} $ rings …

Throughout all rings R are associative wit, h identity, and all modules are unitary right R-
modules. Mod-R will denote the category of unitary right R-modulcs. A classical result in ring …

Let R be an associative ring with identity. We show that every direct sum of singular injective
right R-modules is injective iff any one of the following equivalent conditions holds. i) Every …

An R-module hf is called extending (or a CS-module) if every submodule of M is essential in
a direct summand of M. The module M is called C-eztendzng (resp., finitely or countably C …