Let I be an ideal of a Noetherian ring R and M be a finitely generated R-module. We
introduce the class of extension modules of finitely generated modules by the class of all …

Let R be a commutative Noetherian ring, I an ideal of R, and M a non-zero R-module. The
purpose of this article is to introduce the notation of the nth finiteness dimension for all n∈ …

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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 …

In this paper we shall prove the following result, which is a generalization of the
Melkersson's main result proved in. Let (R, 𝔪) be a Noetherian local ring such that is integral …

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 commutative Noetherian ring, \mathfraka be an ideal of R, n be a non-negative
integer, X be an arbitrary R-module and L be a finitely generated R-module. We characterize …

Let R be a commutative Noetherian ring with identity and I be an ideal of R. Also, let M and N
be two nonzero R-modules. We prove that the R-module E xt R i (N, M) is I-cominimax for all …

Let $\mathfrak {a} $ be an ideal of a commutative noetherian ring $ R $ and $ M, N $ two
finitely generated $ R $-modules. By using a spectral sequence argument, it is shown that if …

Let R be a commutative Noetherian local ring, I an ideal of R, and let M be a non-zero finitely
generated R-module. In this paper, we establish some new properties of the local …