Given modules M and N, M is said to be N-subinjective if for every extension K of N and
every homomorphism φ: N→ M there exists a homomorphism ϕ: K→ M such that ϕ| N= φ …

Absolutely pure modules act in ways similar to injective modules. There are conditions on a
ring which guarantee that the class of injective modules will be covering. In this article, we …

The main results of this paper concern decompositions of an injective module, either as a
direct sum of submodules or as the injective envelope of a direct sum of injective …

In this short paper, the homological functors are used to show that a simple module is flat if
and only if it is injective. It is used to give a characterization of Von Neumann regular ring …

Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …

Let M be a left R-module and F a submodule of M for any ring R. We call MF-semiregular if
for every x∈ M, there exists a decomposition M= A⊕ B such that A is projective, A≤ Rx and …

Recently, there are a number of well known theorems which characterize rings in terms of
injective modules (cf.[2],[3],[5] and [8]). The purpose of this paper is to give general theorems …

A module is said to be P–projective if it is a cokernel of a projective preenvelope. We first
obtain a number of characterizations of P–projectivity. Then we study when the exactness of …

Let R be a ring and M a right R-module. M is called a cofinitely lifting module if for any
cofinite submodule N of M, there exists a direct summand K of M such that K≤ N and N/K≪ …

We show that if M is a finitely generated module over a commutative Noetherian local ring R
and I is a dimension one ideal of R (ie, dim RI= 1), then the local cohomology modules HIi …