Let R be a commutative ring with identity and S a multiplicative subset of R. The aim of this
paper is to study the class of commutative rings in which every S-flat module is flat (resp …

Let R be a ring and M be an R-module. In this paper we investigate modules M such that
every (simple) cosingular R-module is M-projective. We prove that every simple cosingular …

Given a multiplicative subset S in a commutative ring R, we consider S-weakly cotorsion and
S-strongly flat R-modules, and show that all R-modules have S-strongly flat covers if and …

In Bican et al., it is proved that all modules over an arbitrary ring have flat covers. In this
article, we shall study rings over which flat covers of finitely generated modules are …

Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective
hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R …

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 …

In this note we consider a generalization of the notion of a purely extending modules,
defined using y–closed submodules. We show that a ring R is purely y–extending if and only …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

We say that a ring R is a right RDV-ring if each simple right R-module is RD-injective. In this
paper, we study the notion of RDV-rings which is a non-trivial generalization of V-rings and …

Let M be a module. A\delta-cover of M is an epimorphism from a module F onto M with
a\delta-small kernel. A\delta-cover is said to be a flat\delta-cover in case F is a flat module. In …