There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

In this paper, we introduce and study the w-weak global dimension ww. gl. dim (R) of a
commutative ring R. As an application, it is shown that an integral domain R is a Prüfer v …

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 …

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 …

Let R be a commutative ring with identity. Denote by FPR (R) the set of all R-modules
admitting a finite projective resolution consisting of finitely generated projective modules …

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 …

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 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 …

Let $ R $ be a commutative ring. In this paper, the $ w $-projective Basis Lemma for $ w $-
projective modules is given. Then it is shown that for a domain, nonzero $ w $-projective …