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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| Language: | English |
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Lugansk National Taras Shevchenko University
2020
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2021-01-03T08:40:58Z |
| collection |
OJS |
| language |
English |
| topic |
Artinian modules Bass numbers Cousin complexes local cohomology modules minimax modules 13D02 13D03 13D45 13E10 |
| spellingShingle |
Artinian modules Bass numbers Cousin complexes local cohomology modules minimax modules 13D02 13D03 13D45 13E10 Vahidi, A. Modules with minimax Cousin cohomologies |
| topic_facet |
Artinian modules Bass numbers Cousin complexes local cohomology modules minimax modules 13D02 13D03 13D45 13E10 |
| format |
Article |
| author |
Vahidi, A. |
| 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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/528 |
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AT vahidia moduleswithminimaxcousincohomologies |
| first_indexed |
2025-07-17T10:30:19Z |
| last_indexed |
2025-07-17T10:30:19Z |
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1837889823730302976 |