The concept of a module M being almost N-injective, where N is some module, was
introduced by Baba (1989). For a given module M, the class of modules N, for which M is …

In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

We study the rings R for which every R-module is almost injective. For such a ring R, it is
shown that R/Soc (RR) is semisimple and Rad (R) is finitely generated. It is proved that …

We introduce the class of “right almost V-rings” which is properly between the classes of
right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R …

The purpose of this note is to give various conditions that are equivalent to the almost
injectivity of an R-module M relative to an R-module N. These conditions give a unified …

We characterize right Noetherian rings over which all simple modules are almost injective. It
is proved that R is such a ring, if and only if, the complements of semisimple submodules of …

Almost Projective and Almost Injective Modules Page 1 ISSN 0001-4346, Mathematical
Notes, 2018, Vol. 103, No. 1, pp. 3–17. © Pleiades Publishing, Ltd., 2018. Original Russian …

It is shown that every finitely generated right R-module is almost injective if and only if every
cyclic right R-module is almost injective, if and only if R/J (R) is a right SV-ring with Loewy …

This is a brief survey on almost injectivity that has been studied mostly by Harada, and his
collaborators. Baba introduced this concept as a dual to the concept of almost projectivity. In …

For an ideal $\mathcal {I} $ of a preadditive category $\mathcal {A} $, we study when the
canonical functor $\mathcal {C}:\mathcal {A}{\rightarrow}\mathcal {A}/\mathcal {I} $ is local …