In this article, we study the weak global dimension of coherent rings in terms of the left FP-
injective resolutions of modules. Let R be a left coherent ring and ℱ ℐ the class of all FP …

Let R be a commutative coherent ring and wD (R) denote the weak global dimension of R.
We prove that for an integer n≥ 2 the following are equivalent:.(a) wD (R) n;.(b) FP-idM⊗ …

We prove that (a) if R is a left coherent ring, then the weak global dimension w D (R)<= n
(n>= 2) if and only if every (n–2) th F–cosyzygy of a finitely presented right R–module has a …

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 …

Let R be a left coherent ring, S any ring and RωS an (R, S)-bimodule. Suppose ωS has an
ultimately closed FP-injective resolution and RωS satisfies the conditions:(1) ωS is finitely …

Let R be any ring. A right R-module M is called n-copure projective if Ext1 (M, N)= 0 for any
right R-module N with fd (N)≤ n, and M is said to be strongly copure projective if Ext i (M, F) …

The small finitistic dimension of a ring is determined as the supremum projective dimensions
among modules with finite projective resolutions. This paper seeks to establish that, for a …

We study, in this article, the FGT-injective dimensions of Π-coherent rings. If R is right Π-
coherent, and TI (resp. TF) stands for the class of FGT-injective (resp. FGT-flat) R-modules …

Let R be a ring, na fixed non-negative integer and ℱ the class of all left R-modules of FP-
injective dimensions at most n. It is proved that all left R-modules over a left coherent ring R …

We investigate injective dimension of $ F $-finite $ F $-modules in characteristic $ p $ and
holonomic $ D $-modules in characteristic 0. One of our main results is the following. If …