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 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 I be an ideal of a commutative Noetherian ring R such that the R-modules HI i (U) are I-
cofinite, for all finitely generated R-modules U and all i∈ ℕ 0. Also, assume that the category …

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 …

Let R be a commutative Noetherian ring with non-zero identity, na non-negative integer, 𝔞
an ideal of R with dim (R/𝔞)≤ n+ 1, and X an arbitrary R-module. In this paper, we prove the …

Let I be an ideal of a commutative Noetherian ring R such that the R-modules HI i (M) are I-
cofinite, for all finitely generated R-modules M and all i∈ ℕ 0. Let M and N be two I-cofinite R …

Let $ R $ be a commutative Noetherian ring with non-zero identity, $\mathfrak {a} $ and
$\mathfrak {b} $ ideals of $ R $ with $\mathfrak {a}\subseteq\mathfrak {b} $, and $ M $ a …

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 …

Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules HI j (M)
are I-cofinite for all finitely generated R-modules M and all j∈ ℕ0 if and only if the R …

Let R be a Noetherian ring, I an ideal of R and M an R-module. It is shown that if Ext R i (R/I,
M) Ext^i_R(R/I,M) is finitely generated, for all i≤ dim M, then Ext R i (N, M) Ext^i_R(N,M) is …