We studied almost relative projective modules and almost relative injective modules in [3, 6,
7]. In this short note we define a new module, an almost projective (resp. almost injective) …

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 …

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

Let R be a ring and M a fixed R-module. An R-module Q is called M-injective if, given a
monomorphism C $ of an R-module N into M, every homomorphism: N-+ Q can be extended …

We have introduced a concept of almost relative projectives (resp. injectives) in [7](resp.[2])
which is deeply related with lifting modules [9](resp. extending modules [10]). When we …

ABSTRACT A right R-module M is called simple-direct-injective if, whenever, A and B are
simple submodules of M with A≅ B, and B⊆⊕ M, then A⊆⊕ M. Dually, M is called simple …

In this paper, we introduce and study the dual notion of simple-direct-injective modules.
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …

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 …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

Let $ R $ be a commutative ring with identity and $ D $ an $ R $-module. It is shown that if $
D $ is pure injective, then $ D $ is isomorphic to a direct summand of the direct product of a …