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 …

This book surveys more than 125 years of aspects of associative algebras, especially ring
and module theory. It is the first to probe so extensively such a wealth of historical …

A right R-module M is called quasi-principally injective if every homomorphism from an M-
cyclic submodule of M to M can be extended to M. Let M be a quasi-principally injective …

Let $ R $ be a ring and $ E= E (R_R) $ its injective envelope. We show that if every simple
right $ R $-module embeds in $ R_R $ and every cyclic submodule of $ E_R $ is essentially …

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 …

A module M is said to be weakly injective if every finitely generated submodule of its
injective hull E (M) is contained in a submodule X of E (M) isomorphic to M. We prove that a …

The notation in this paper will be standard and it may be found in [2] or [8]. Throughout the
paper, the notation A⊂'B will mean that A is an essential submodule of the module B. Given …

Throughout the following, R will always denote a ring with multiplicative identity 1 and all
modules will be taken from the category R--mod of unitary left R-modules. Morphisms in R …

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) …