… 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 …

… 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 over …

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 …

… 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 …

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, …

A module M is said to be lifting if, for any submodule X of M , there exists a decomposition M
= A ⊕ B such that A ⊆ X and X / A is a small submodule of M / A . A lifting module is defined …