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 …

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 …

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 …

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) …

440 L. Eo T, WU AND $. Po SANS properties of quasi invectives. In Section 2, we list some
of these properties supplying proof only where it isn't obvious how to dualize from the quasi …

Characterization of Rings Using Quasiprojective Modules. II Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 28, Number 2, May 1971 CHARACTERIZATION …

The restricted injective envelopes with respect to various types of preradicals have been
studied by many authors (see eg [2],[6],[8],[10]). In the second paragraph we shall dualize …

Y. Utumi obtainedthat ifa ring R is left self-injective then so is the residue class ring R/J
modulo the Jacobsn radical J of R. And BL Osofsky [5] extended this result to the case of …

An useful tool in the study of the endomorphism ring S of a quasi-injective left R-module U is
the duality defined by RUS which has been recently investigated in several papers ([7],[15]) …