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 …

It is shown that, over any ring R, the direct sum M=⊕ i∈ IMi of uniform right R-modules Mi
with local endomorphism rings is a CS-module if and only if every uniform submodule of M is …

A module M is called extending if, for any submodule X of M, there exists a direct summand
of M which contains X as an essential submodule, that is, for any submodule X of M, there …

A module M over a ring R is called a lifting module if every submodule A of M contains a
direct summand K of M such that A/K is a small submodule of M/K (eg, local modules are …

Almost N-projective modules and generalized N-projective modules play an important role
in the study of lifting modules and artinian rings. In this paper, we study a relationship …

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 …

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 …

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 …

3704 JAYARAMAN AND VANAJA prove that in this case there exists a module (in fact a
direct suninlarid of A1 which is projective in a [iLl] if fll is fg) NE a [ill] such that a [N]= a [i\l], iV …

In this note, we introduce the (small, pseudo-) ℬ (M, X)-cojective modules and we generalize
(small, pseudo-) cojective modules via the class ℬ (M, X). Let M= M1⊕ M2 be an X-amply …