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 …

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 …

An R-module hf is called extending (or a CS-module) if every submodule of M is essential in
a direct summand of M. The module M is called C-eztendzng (resp., finitely or countably C …

The references are Bass [B], Roberts [R₁],[R₂], Foxby and Thorup [FT], and Foxby
[F],[F₂],[F], but further comments on the results will be provided in the subsequent sections …

Our concern is with modules M such that every homomorphism from a closed submodule of
M to M can be lifted to M. Although such modules share some of the properties of extending …

A module is said to be copure injective if it is injective with respect to all modules A⊂ B with
B/A injective. We first characterize submodules that have the extension property with respect …

Let MR denote a right module over a ring R; MR is unital in case B has an identity element
which is the identity operator on M. A module (resp. unital module) MR is injeetive (resp …

LEMMA 7. Suppose M=:~ a~ A~,, E,,= E (:] L~), E~@ a~ AEr E is an injective module, and M~
is an Mb-injective module for all a=/= b. Then: a) if each module M~ is quasiinjective, then M …

The notation in this paper will be standard and it may be found in [2] or [8]. Throughout the
paper, the notation A⊂'B will mean that A is an essential submodule of the module B. Given …

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 …