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. 
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     title = {Modules with minimax {Cousin} cohomologies},
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     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/

[1] K. Bahmanpour, R. Naghipour, “On the cofiniteness of local cohomology modules”, Proc. Amer. Math. Soc., 136 (2008), 2359–2363 | DOI | MR | Zbl

[2] M. P. Brodmann, R. Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Cambridge University Press, Cambridge, 1998 | MR | Zbl

[3] W. Bruns, J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, Cambridge, 1998 | MR | Zbl

[4] M. T. Dibaei, M. Tousi, “The structure of dualizing complex for a ring which is ($S_2$)”, J. Math. Kyoto Univ., 38 (1998), 503–516 | MR | Zbl

[5] M. T. Dibaei, M. Tousi, “A generalization of the dualizing complex structure and its applications”, J. Pure Appl. Algebra, 155 (2001), 17–28 | DOI | MR | Zbl

[6] M. T. Dibaei, “A study of Cousin complexes through the dualizing complexes”, Comm. Algebra, 33 (2005), 119–132 | DOI | MR | Zbl

[7] M. T. Dibaei, R. Jafari, “Modules with finite Cousin cohomologies have uniform local cohomological annihilators”, J. Algebra, 319 (2008), 3291–3300 | DOI | MR | Zbl

[8] R. Hartshorne, Residues and Duality, Springer, 1966 | MR | Zbl

[9] C. Huneke, Problems on Local Cohomology: Free Resolutions in Commutative Algebra and Algebraic Geometry, Jones and Bartlett, 1992 | MR

[10] T. Kawasaki, “Finiteness of Cousin cohomologies”, Trans. Amer. Math. Soc., 360 (2008), 2709–2739 | DOI | MR | Zbl

[11] J. Lipman, S. Nayak, P. Sastry, “Pseudofunctorial behavior of Cousin complexes on formal schemes”, Contemp. Math., 375 (2005), 3–133 | DOI | MR | Zbl

[12] J. Rotman, An Introduction to Homological Algebra, Academic Press, 1979 | MR | Zbl

[13] R. Y. Sharp, “The Cousin complex for a module over a commutative Noetherian ring”, Math. Z., 112 (1969), 340–356 | DOI | MR | Zbl

[14] R. Y. Sharp, “Gorenstein modules”, Math. Z., 115 (1970), 117–139 | DOI | MR | Zbl

[15] R. Y. Sharp, “Cousin complex characterizations of two classes of commutative Noetherian rings”, J. London Math. Soc., 3 (1971), 621–624 | DOI | MR | Zbl

[16] H. Zöschinger, “Minimax Moduln”, J. Algebra, 102 (1986), 1–32 | DOI | MR | Zbl