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Modules with minimax Cousin cohomologies
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 p of R and for every integer n less than X—the height of p:...
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Інститут прикладної математики і механіки НАН України
2020
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| Series: | Algebra and Discrete Mathematics |
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irk-123456789-1885582023-03-06T01:27:05Z Modules with minimax Cousin cohomologies Vahidi, A. 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 p of R and for every integer n less than X—the height of p: (i) the nth Bass number of X with respect to p is finite; (ii) the nth local cohomology module of Xp with respect to pRp is Artinian. 2020 Article Modules with minimax Cousin cohomologies / A. Vahidi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 143–149. — Бібліогр.: 16 назв. — англ. 1726-3255 DOI:10.12958/adm528 2010 MSC: 13D02, 13D03, 13D45, 13E10. http://dspace.nbuv.gov.ua/handle/123456789/188558 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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English |
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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 p of R and for every integer n less than X—the height of p: (i) the nth Bass number of X with respect to p is finite; (ii) the nth local cohomology module of Xp with respect to pRp is Artinian. |
| format |
Article |
| author |
Vahidi, A. |
| spellingShingle |
Vahidi, A. Modules with minimax Cousin cohomologies Algebra and Discrete Mathematics |
| author_facet |
Vahidi, A. |
| author_sort |
Vahidi, A. |
| title |
Modules with minimax Cousin cohomologies |
| title_short |
Modules with minimax Cousin cohomologies |
| title_full |
Modules with minimax Cousin cohomologies |
| title_fullStr |
Modules with minimax Cousin cohomologies |
| title_full_unstemmed |
Modules with minimax Cousin cohomologies |
| title_sort |
modules with minimax cousin cohomologies |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188558 |
| citation_txt |
Modules with minimax Cousin cohomologies / A. Vahidi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 143–149. — Бібліогр.: 16 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT vahidia moduleswithminimaxcousincohomologies |
| first_indexed |
2023-10-18T23:08:38Z |
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2023-10-18T23:08:38Z |
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1796157360841949184 |