This unique and comprehensive volume provides an up-to-date account of the literature on
the subject of determining the structure of rings over which cyclic modules or proper cyclic …

Because traditional ring theory places restrictive hypotheses on all submodules of a module,
its results apply only to small classes of already well understood examples. Often, modules …

We survey results on the theory of weakly-injective modules obtained during the last five
years. In particular, we show that arbitrary direct sums of weakly-injective right modules are …

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 …

The direct sum decomposition of torsion free, ie, nonsingular modules, into direct summands
belonging to saturated classes of modules is developed here for the first time for arbitrary not …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

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 …

We consider two types of weak-injectivity domains of a module. Small weak-injectivity
domains gauge the extent of weak injectivity of modules; weak-injectivity domains are an …

Introduction. Recently the concept of weakly injective modules due to [ll] has extensively
been studied and used to characterize various rings and modules; see [I-3, 5, 10-14, 16-18 …

A module M is said to be wealdy-injective if and only if for every finitely generated
submodule N of the injective hull E (M) of M there exists a submodule X of E (M), isomorphic …