We have defined aconcept of almost M-projectives and almost M-injectives in [4] and [9],
respectively. In the first section of this paper we give some relations among lifting modules …

In 1960, H. Bass [3] defined the notion of semi-perfect rings and, in 1963, E. Mares [ll]
generalized it to that of semi-perfect modules. Since that time various kinds of further …

Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …

Recently, in [2], Harada and Tozaki defined'almost M-projectives* which are generalized
from the concept'M-projectives' due to Azumaya. In this paper we shall define a dual …

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 …

We have defined a new concept of almost M-projectives [7] and given several properties of
them [4]. This paper is a continuous work of [4] and [7]. If a module MQ is Mrprojective for a …

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) …

We studied almost relative projective modules and almost relative injective modules in [3, 6,
7]. In this short note we define a new module, an almost projective (resp. almost injective) …

Quasi-principally injective modules were studied in [12]. In this note we introduce the
concept dual to quasi-principally injective modules. It is proved that. these modules are …