Given an R-module C and a class of R-modules 𝒟 over a commutative ring R, we investigate
the relationship between the existence of 𝒟-envelopes (respectively, 𝒟-covers) and the …

Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …

In this paper, we introduce and study the concepts of weak n-injective and weak n-flat
modules in terms of super finitely presented modules whose projective dimension is at most …

Let R be a commutative ring, M an R-module, and N a finitely presented R-module such that
the intersection of Max (R) and Supp (N) is finite-dimensional and Noetherian. Suppose also …

Given an arbitrary quasiprojective right R-module P, we prove that every module in the
category σ (P) is weakly regular if and only if every module in σ (M/I (M)) is lifting, where M is …

We prove that (a) if R is a left coherent ring, then the weak global dimension w D (R)<= n
(n>= 2) if and only if every (n–2) th F–cosyzygy of a finitely presented right R–module has a …

Given modules M and P, we introduce in section 2 the concept of an (M, P)-injective module.
This concept contains many versions of injectivity known in the literature, such as principal …

ABSTRACT A right R-module M is called a U-module if, whenever A and B are submodules
of M with A≅ B and A∩ B= 0, there exist two summands K and L of M such that A⊆ ess K …

In this paper, we introduce and study a generalization of coretractable modules. An R-
module M is called coretractable relative to an R-module N if Hom R (M/X, N)≠ 0, for any …

Let R be a local ring and C a semidualizing module of R. We investigate the behavior of
certain classes of generalized Cohen-Macaulay R-modules under the Foxby equivalence …