Geodesic
Modules with minimax Cousin cohomologies
Algebra and discrete mathematics, Tome 30 (2020) no. 1, pp. 143-149

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Let $R$ be a commutative Noetherian ring with non-zero identity and let $X$ be an arbitrary $R$-module. In this paper, we show that if all the cohomology modules of the Cousin complex for $X$ are minimax, then the following hold for any prime ideal $\mathfrak{p}$ of $R$ and for every integer $n$ less than $X$—the height of $\mathfrak{p}$: (i) the $n$th Bass number of $X$ with respect to $\mathfrak{p}$ is finite; (ii) the $n$th local cohomology module of $X_\mathfrak{p}$ with respect to $\mathfrak{p}R_\mathfrak{p}$ is Artinian.
Keywords: Artinian modules, Bass numbers, Cousin complexes, local cohomology modules, minimax modules. 
@article{ADM_2020_30_1_a10,
     author = {A. Vahidi},
     title = {Modules with minimax {Cousin} cohomologies},
     journal = {Algebra and discrete mathematics},
     pages = {143--149},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a10/}
}
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A. Vahidi. Modules with minimax Cousin cohomologies. Algebra and discrete mathematics, Tome 30 (2020) no. 1, pp. 143-149. http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a10/