The concept of weak relative-injectivity of modules was introduced in [6] in order to study
rings all of whose cyclic modules are embeddable as essential submodules of projective …

If R is a hereditary left artinian ring, then R is left pure semisimple if and only if the family R-
ind of all finitely generated indecomposable left R-modules has a (unique) Ext-injective …

If $ R $ is a ring and $ P $ is a finitely generated projective right $ R $-module, what
properties of $ R $ does the $ R $-endomorphism ring of $ P $ inherit? Rosenberg and …

In this paper certain injectivity conditions in terms of extensions of monomorphisms are
considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if …

An R-module M is called strongly FP-injective if Ext R i (P, M)= 0 for any finitely presented R-
module P and any i> 0. Denoted by SFI the class of all strongly FP-injective R-modules and …

1. Let R be a ring with identity not equal to zero. A right R-module is said to be quasi-
injective (pseudo-injective) if for every submodule N of M, every R-homomorphism (R …

Let R be a ring with identity element and M be a unitary left R-module. M is called quasi-
injective if every element in Hom^ Af, M) for any R-module N in M is extened to an element in …

Rosenberg and Zelinsky [6] first addressed the question of characterizing for a ring R those
simple modules RT having injective hulls of finite length. In that work they also announced a …

Because F is a free module of infinite rank we see that F^ Fn all n^ l. It follows that H^ Hn as
right (or left) H-modul es. So H is isomorphic (as ring) to Hn, forali n> 1. Further every finitely …

In this paper, unless otherwise indicated, we shall not assume that our rings are
commutative, but we shall always assume that every ring has an identity element. By a …