For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

Recall that a ring A is called quasi-Frobenius if it is artinian and self-injective on both sides
(see eg 17, 81,[2],[3] and [6]). In this note, following Yukimoto [ill, we call a ring A strongly …

Introduction. A ring is called left (right) hereditary in case each left (right) ideal is projective.
Such rings have been studied extensively, and the property of being left hereditary is …

A ring R is called left IP-injective if every homomorphism from a left ideal of R into R with
principal image is given by right multiplication by an element of R. It is shown that R is left IP …

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 …

The purpose of this paper is to initiate the study of improjective modules. A module X is im-
projective if given any epimorphism/: B-> A and any homomorphism/: X-> A, there exists a …

This paper was motivated by one of Armendariz and Park [I] in which it is proved that a left
self-injective ring R is quasi-Frobenius (QF) if the factor ring of R modulo its left (or right) …

Weakening the notion of R-projectivity, a right R-module M is called max-projective provided
that each homomorphism f: M→ R/I, where I is any maximal right ideal, factors through the …