A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

Let R be a commutative ring with identity. An R-module M is said to be w-projective if Ext1 R
(M, N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w …

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, S a multiplicative subset of R. An R-module M is said to be uS-flat (u-always
abbreviates uniformly) if \Tor^R_1(M,N) is uS-torsion R-module for all R-modules N. In this …

It is proven that the weak dimension of each FP-injective module over a chain ring which is
either Archimedean or not semicoherent is less or equal to 2. This implies that the projective …

In this paper, we characterize w‐Noetherian rings and SM rings. More precisely, in terms of
the u‐operation on a commutative ring R, we prove that R is w‐Noetherian if and only if the …

R is called a right ${\Pi}-coherent $ ring in case every finitely generated torsion less right R-
module is finitely presented. In this paper, we define a dimension for rings, called ${\Pi} …

Using U-torsionless module we characterize U-neat submodules and Au-injective modules.
If M is a left R-module, U is E (M)-injective and Eu (M)/M does not contain a nonzero …

For a ring R, we prove that all left R-modules have weak injective covers and weak injective
preenvelopes. Then we characterize the right weak injective dimension of modules in terms …