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 \(\mathfrak{p}\) of \(R\) and for every in...
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2020
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/528 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543310518157312 |
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| author | Vahidi, A. |
| author_facet | Vahidi, A. |
| author_sort | Vahidi, A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-01-03T08:40:58Z |
| 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 \(\mathfrak{p}\) 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. |
| first_indexed | 2025-12-02T15:26:55Z |
| format | Article |
| id | admjournalluguniveduua-article-528 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:26:55Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-5282021-01-03T08:40:58Z Modules with minimax Cousin cohomologies Vahidi, A. Artinian modules, Bass numbers, Cousin complexes, local cohomology modules, minimax modules 13D02, 13D03, 13D45, 13E10 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. Lugansk National Taras Shevchenko University 2020-12-30 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/528 10.12958/adm528 Algebra and Discrete Mathematics; Vol 30, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/528/pdf Copyright (c) 2020 Algebra and Discrete Mathematics |
| spellingShingle | Artinian modules Bass numbers Cousin complexes local cohomology modules minimax modules 13D02 13D03 13D45 13E10 Vahidi, A. Modules with minimax Cousin cohomologies |
| 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 |
| topic | Artinian modules Bass numbers Cousin complexes local cohomology modules minimax modules 13D02 13D03 13D45 13E10 |
| topic_facet | Artinian modules Bass numbers Cousin complexes local cohomology modules minimax modules 13D02 13D03 13D45 13E10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/528 |
| work_keys_str_mv | AT vahidia moduleswithminimaxcousincohomologies |