Let $ R $ be a commutative ring. An $ R $-module $ M $ is called a semi-regular $ w $-flat
module if $\Tor_1^ R (R/I, M) $ is $\GV $-torsion for any finitely generated semi-regular ideal …

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 …

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. An R-module M is said to be an absolutely w-pure module if
Ext R 1 (F, M) is GV-torsion for any finitely presented R-module F. In this paper, we further …

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 …

Let $ R $ be a commutative ring. An $ R $-module $ M $ is said to be $ w $-flat if $\Tor^{R} _
{1}(M, N) $ is $ GV $-torsion for any $ R $-module $ N $. It is known that every flat module is …

Let $ R $ be a ring. An $ R $-module $ M $ is said to be an absolutely $ w $-pure module if
and only if $\Ext^ 1_R (F, M) $ is a GV-torsion module for any finitely presented module $ F …

Let R be a commutative ring with identity. In this paper, w∞-projective modules are
introduced and studied. It is shown that every R-module has a special w∞-projective …

Let $ R $ be a ring. An $ R $-module $ M $ is said to be a weak $ w $-projective module if
${\rm Ext} _R^ 1 (M, N)= 0$ for all $ N\in\mathcal {P} _ {w}^{\dagger_\infty} $(see,\cite {FLQ}) …

Let R be an integral domain, K= qf (R) and F (R) the set of fractional ideals of R. Let GV
(R)={I| I a finitely generated ideal with I− 1= R}. For a torsion-free R-module M, define M …