Recently,]~. DE ROBERT has considered the dual concepts of relative projectivity and
relative injectivity that extend the notions of quasi-projective and quasi-injective modules …

Introduction and notation. Throughout this paper all rings are associative rings with identity
and all modules are unitary left modules. An R-module M is quasi-injective in case HomR …

In this paper $ R $ denotes an associative ring with an identity, and all modules are unital
left $ R $-modules. It is shown that the existence of a quasi-projective cover for each module …

This paper is supplemental to [4],[6] and [7]. We shall show, under assumption of finite
length, that when we study almost relative projectives, we may restrict ourselves only to …

If M denotes the class of unitary left modules over a ring R, then each subclass# ofM
determines two subclasses ofJt—the relative projectivity class and the relative injectivity …

M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …

Endomorphism rings of projective and quasiprojective modules (and in particular the
problem of finding conditions on a module for its endomorphism ring to have a certain …

We have defined a new concept of almost relative projectivity [7], If a module Mo is M,-
ρrojective for a finite set of modules Miy then Mo is 2,-φ Λff-projective [2]. However this fact is …

In this paper we shall generalize the notion of semiperfect modules in terms of preradicals,
and show that almost all properties of semiperfect modules are preserved under this …