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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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188558 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modules with minimax Cousin cohomologies / A. Vahidi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 143–149. — Бібліогр.: 16 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862534771700137984 |
|---|---|
| author | Vahidi, A. |
| author_facet | Vahidi, A. |
| citation_txt | Modules with minimax Cousin cohomologies / A. Vahidi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 143–149. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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.
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| first_indexed | 2025-11-24T09:25:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188558 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T09:25:50Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Vahidi, A. 2023-03-05T17:40:08Z 2023-03-05T17:40:08Z 2020 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. https://nasplib.isofts.kiev.ua/handle/123456789/188558 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. This research was in part supported by a grant from Payame Noor University en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Modules with minimax Cousin cohomologies Article published earlier |
| spellingShingle | Modules with minimax Cousin cohomologies Vahidi, A. |
| title | 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_short | Modules with minimax Cousin cohomologies |
| title_sort | modules with minimax cousin cohomologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188558 |
| work_keys_str_mv | AT vahidia moduleswithminimaxcousincohomologies |