Let R be a commutative ring. If the nilpotent radical N il (R) of R is a divided prime ideal, then
R is called a ϕ-ring. In this paper, we first distinguish the classes of nonnil-coherent rings …

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 paper, the notions of nonnil-injective modules and nonnil-FP-injective modules are
introduced and studied. Especially, we show that a $\phi $-ring $ R $ is an integral domain if …

In this paper, we first introduce and study the notions of strongly $\phi $-flat modules and
strongly nonnil-injective modules. And then, we investigate the homology dimensions of …

In this paper, we introduce and study the class of $\phi $-$ w $-P-flat modules, which can be
seen as generalizations of both $\phi $-P-flat modules and $ w $-P-flat modules. In …

In this paper, we introduce and study the notion of strongly $\phi $-$ w $-flat modules. The
$\phi $-$ w $-weak global dimension $\phi $-$ w $-w. gl. dim $(R) $ of an NP-ring $ R $ is …

This paper introduces and studies the ϕ-uS-flat (resp., nonnil-uS-injective) modules, which
are a generalization of both ϕ-flat modules and uS-flat modules (resp., both nonnil-injective …

Recently, Zhao, Wang, and Pu introduced and studied new concepts of nonnil-commutative
diagrams and nonnil-projective modules. They proved that an R-module that is nonnil …

In this note, we show that a strongly φ-ring R is a φ-PvMR if and only if any φ-torsion-free R-
module is φ-w-flat, if and only if any GV-torsion-free divisible R-module is nonnil-absolutely …

In this note, we show that a strongly $\phi $-ring $ R $ is a $\phi $-PvMR if and only if any
$\phi $-torsion free $ R $-module is $\phi $-$ w $-flat, if and only if any divisible module is …