The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules
with respect to a multiplicative subset or a finite collection of multiplicative subsets in a …

The mono-epi (ME) exact structure on the morphisms of an exact category is introduced and
used to prove ideal versions of Salce's Lemma, Christensen's (Ghost) Lemma, and …

In this paper, we prove that the Bass class with respect to a semidualizing bimodule C
contains all FP-injective S-modules. We introduce the definition of C-FP-injective modules …

Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-
injective if Ext d+ 1 R (P, M)= 0 for any n-presented R-module P. M is said to be (n, d) …

A left R-module M is said to be mininjective if Ext1 (R/I, M)= 0 for any simple left ideal I of R.
A ring R is called left min-coherent in case each simple left ideal of R is finitely presented. It …

A submodule N of a right R-module M is called coneat if for every simple right R-module S,
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …

Let R be a ring. A left R-module M is said to be min-injective if for any simple left ideal I. A
right R-module N is called min-flat if for any simple left ideal I. R is said to be a left min …

In this article, several characterizations of certain classes of rings via FC-purity and I-purity
are considered. Among others results, it is shown that every I-pure injective left R-module is …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …