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CHARACTERIZATION OF WEAKLY COFINITE LOCAL COHOMOLOGY MODULES
Moharram Aghapournahr,Marziye Hatamkhani Korean Mathematical Society 2023 대한수학회보 Vol.60 No.3
Let R be a commutative Noetherian ring, 𝔞 an ideal of R, M an arbitrary R-module and X a finite R-module. We prove a characterization for H<sup>i</sup><sub>𝔞</sub>(M) and H<sup>i</sup><sub>𝔞</sub>(X, M) to be 𝔞-weakly cofinite for all i, whenever one of the following cases holds: (a) ara(𝔞) ≤ 1, (b) dim R/𝔞 ≤ 1 or (c) dim R ≤ 2. We also prove that, if M is a weakly Laskerian R-module, then H<sup>i</sup><sub>𝔞</sub>(X, M) is 𝔞-weakly cofinite for all i, whenever dim X ≤ 2 or dim M ≤ 2 (resp. (R, m) a local ring and dim X ≤ 3 or dim M ≤ 3). Let d = dim M < ∞, we prove an equivalent condition for top local cohomology module H<sup>d</sup><sub>𝔞</sub>(M) to be weakly Artinian.