In this paper, we introduce and study the class of $\phi $-$ w $-flat modules which are
generalizations of both $\phi $-flat modules and $ w $-flat modules. The $\phi $-$ w $-weak …

Let R be a commutative ring and w be the so-called w-operation on R. Then we introduce
and study two concepts of w-FP-injective modules and w-IF rings. To do so, we use two main …

The w-operation, which is in some respects a “better behaved” variant of the classic t-
operation, has recently been an object of intense study. In this article, we introduce and …

In this article, we provide several descriptions of w-coherent rings in terms of modules. We
show that a ring R is w-coherent if and only if every direct product of flat modules is w-flat. To …

In this article, we introduce a new type of projective modules, called the weak w-projective
module. By using this type of modules, we give a homological characterization of Krull …

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the
natural homomorphism I⊗ RM→ R⊗ RM is a w-monomorphism for any regular ideal I. We …

Let R be a commutative ring with identity. Denote by w𝒫 w the class of weak w-projective R-
modules and by w𝒫 w⊥ the right orthogonal complement of w𝒫 w. It is shown that (w𝒫 w …

It is well known in [Absolutely pure modules, Proc. Amer. Math. Soc. 26 (1970) 561–566,
Theorem 6] that a domain R is a Prüfer domain if and only if every divisible R-module is …

It is well known that a domain R is a Prüfer domain if and only if for R-modules, relative
divisibility implies purity. In this paper, we extend this result to Prüfer v-multiplication …

Let R be a commutative ring. An R-module M is said to be w-flat if TorR 1 (M, N) is a GV-
torsion R-module for all R-modules N. In this paper, we study the flat and projective …