… In this note, we investigate the relationship between almost projective modules and … M and
N, then M is almost N-projective. We also show that if M is almost N-projective and N is lifting, …

… for an N-almost-invariant module to be almost N-injective. Moreover, we study a relationship
between generalized N-injective, almost N-injective and N-almost-invariant modules. …

… A module M is said to be almost-injective (almost self-injective) if it is almost injective with
respect to every right R-module (respectively, almost M-injective). The class of …

… R for which every simple module is almost injective, ie, R is an almost V-ring, the class 2
stands for all rings R for which every semisimple module is almost injective, the class 3 stands …

… As an immediate consequence of the definition of almost relative injectives, we obtain that
if a module MR is almost NR-injective, then M is essentially N-injective. For details on rings …

… The next lemma shows that this is also true if a direct sum of modules is nearly injective. …
Harada , On almost M-projectives and almost M-injectives, Tsukuba J. Math. 14, 53–69 (1990) G…

X. A module M is said to satisfy the finite internal exchange property if, for any direct summand
X of M and any finite direct sum decomposition M = ⊕^ni=1 Mi, there exists Mi ⊆ Mi (i = 1, …

In this study, it is investigated the relation between almost projective modules and generalized
projective modules. These concepts are useful for the study on finite direct sum of lifting …

Since Azumaya introduced the notion of A-injectivity in 1974, several generalizations have
been investigated by a number of authors. We introduce some more generalizations and …

… covering topics such as: ring theory, with both the elementwise and more structural approaches
developed; module theory with popular topics such as automorphism invariance, almost …