… -module is RD-injective (or, R is Köthe), it suffices to test only the RD-injectivity of the simple
left R-modules. … In the same way we prove that R ′ is cyclic. Since R ′ is the direct limit of a …

… the definition of injective module. An injective module is a module with the largest possible
… the study of a semisimple module to that of cyclic submodules of factor modules. Its proof is …

… every simple module is either injective or furthest from being injective, in some certain senses.
In … cyclic modules have injectivity domains which are coatoms in the lattice of domains of …

… Over such rings, we have that a module has zero radical if and only if so do all its cyclic
submodules (see Lemma 4). We also show that over a commutative hereditary Noetherian ring, a …

… We prove that the rings whose cyclic right modules are indigent are semisimple Artinian.
We … a Whitehead test module for injectivity (i-test module) as follows: A module M is an i-test …

… are given. Finally, we study the singly flatness and singly injectivity of homomorphism
modules … Indeed, let A be a singly injective left R-module and C a cyclic submodule of a finitely …

… An injective module is called elementary if it coincides with the injective envelope of some
cyclic submodule. Such modules form a set and every injective module can be embedded in a …

… If N is the direct sum of a complete set of non-isomorphic cyclic modules in σ[Z ], then σ[Z ]
= σ[N]. Also, if Z is a hereditary pretorsion class, then we have σ[Z ] = Z . This implies that if T is …

… of other properties (projectivity, flatness, weak-injectivity, etc.) Our … a ring is determined by
the injectivity of certain modules, we aim to … for every cyclic submodule C of N, we see that In …

… module can be decomposed into a finite chain of submodules, the successive quotients of
which are cyclic modules and hence isomorphic to some / RI . … connection among flatness and …