Recall that a module M is called distributive if K∩(L+ N)= K∩ L+ K∩ N for any submodules
K, L, N. Clearly, submodules and quotient modules of a distributive module are distributive …

Let R be a commutative ring with identity. A proper submodule N of an R-module M will be
called prime [resp. n-almost prime], if for r∈ R and a∈ M with ra∈ N [resp. ra∈ N\(N: M) n …

Let M be a right R-module. A right R-module N is called pseudo-Mc-injective if for any
monomorphism from a closed submodule of M to N can be extended to homomorphism from …

A unitary left R-module M over a left noetherian ring R with identity is called admissible if
every prime ideal of R, which is the left annihilator of all nonzero submodules of a …

It is known that every essential extension of a direct sum of injective hulls of simple R-
modules is a direct sum of injective R-modules if and only if the ring R is right noetherian …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …

The notion of T-noncosingularity of a module has been introduced and studied recently. In
this article, a number of new results of this property are provided. It is shown that over a …

In this paper, we introduce the concept of NN-torsion-free modules (respectively, NN-
injective modules) as a generalization of nonnil-torsion-free modules (respectively, injective …

Let $ R $ be a commutative unital ring and $ N $ be a submodule of an $ R $-module $ M $.
The submodule $\langle E_M (N)\rangle $ generated by the envelope $ E_M (N) $ of $ N …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …