In [KR Fuller, on indecomposable injectives over artinian rings, Pacific J. Math. 29 (1969),
115-135, Theorem 3.1] KR Fuller gave necessary and sufficient conditions for projective left …

We have introduced a concept of almost relative projectives (resp. injectives) in [7](resp.[2])
which is deeply related with lifting modules [9](resp. extending modules [10]). When we …

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 …

Mathematical Journal of Okayama University Page 1 Mathematical Journal of Okayama
University Volume 51, Issue 1 2009 Article 6 A NOTE ON ALMOST 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 …

It is well known that over a left Notherian ring any direct sum of injecive modules is again
injective, and every injective module is a direct sum of indecomposable modules. Faith [6] …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …

1. Introduction and Statement of the Problem Recent important results in the area of quotient
rings (as in [U, 5, 6, 7, 13]) are based on certain interesting homological notions and results …