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 …

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 …

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) …

Responding to a question on right weakly semisimple rings due to Jain, Lopez-Permouth
and Singh, we report the existence of a non-right-Noetherian ring R for which every uniform …

The notation in this paper will be standard and it may be found in [3], for example. In
particular, the notation A⊂′ B stands for the statement “A is an essential submodule of B” …

ABSTRACT A module M Is said to be weakly projective If and only If It has a projective cover
11": P (M)--+ M and every map from P (M) Into a finitely generated (free) module can be …

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 …