Given a positive integer n, a left R-module M is called n-coherent (resp. n-semihereditary) if
every n-generated submodule of M is finitely presented (resp. projective). We investigate the …

Let R be a commutative Noetherian ring, I⊆ J be ideals of R and M be a finitely generated R-
module. In this paper it is shown that q (J, M)≤ q (I, M)+ cd (J, M/IM). Furthermore, it is shown …

Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules Tor i R
(N, M) are I-cofinite for all i≥ 0 if M and N are I-cofinite R-modules and N is of dimension at …

Let R be a ring, τ= T, ℱ a hereditary torsion theory of mod‐R, and na positive integer. Then,
R is called right τ‐n‐coherent if every n‐presented right R‐module is (τ, n+ 1)‐presented …

Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely
generated R-module. It is shown that the R-modules $ Tor_ {i}^{R}(N, M) $ are I-cofinite for …

Let R be a commutative Noetherian ring, I an ideal of R and let M and N be non-zero R-
modules. It is shown that the R-modules ExtRi (N, M) are I-cofinite, for all i⩾ 0, whenever M is …

In this paper, we introduced two concepts. A module M is said to be purely quasi-injective
(resp. quasi-cotorsion) if it is fully invariant in its pure-injective envelope (resp. if it is flat and …

If R is a right coherent ring, then left R-modules have covers by submodules of flat R-
modules if and only if all injective left R-modules have flat covers. This is the case if R is …

Let R be a commutative Noetherian ring, I an ideal of R, and M an arbitrary R-module. It is
shown that the R-module is finitely generated, for all i≥ 0, if and only if the R-module is …

An R-module M is called strongly FP-injective if Ext R i (P, M)= 0 for any finitely presented R-
module P and any i> 0. Denoted by SFI the class of all strongly FP-injective R-modules and …