A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since
then, these classical artinian rings have continued to fascinate ring theorists with their …

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 …

For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

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 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 …

A ring R is called right simple-injective if every itMinear map with simple image from a right
ideal to R can be extended to R. We characterize when matrix rings, upper triangular matrix …

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 …

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 …