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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| Дата: | 2020 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/528 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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