Article
| Title: | Local cohomology, cofiniteness and homological functors of modules (English) |
| Author: | Bahmanpour, Kamal |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 2 |
| Year: | 2022 |
| Pages: | 541-558 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $I$ be an ideal of a commutative Noetherian ring $R$. It is shown that the $R$-modules $H^j_I(M)$ are $I$-cofinite for all finitely generated $R$-modules $M$ and all $j\in \Bbb {N}_0$ if and only if the $R$-modules ${\rm Ext}^i_R(N,H^j_I(M))$ and ${\rm Tor}^R_i(N,H^j_I(M))$ are $I$-cofinite for all finitely generated $R$-modules $M$, $N$ and all integers $i,j\in \Bbb {N}_0$. (English) |
| Keyword: | cofinite module |
| Keyword: | cohomological dimension |
| Keyword: | ideal transform |
| Keyword: | local cohomology |
| Keyword: | Noetherian ring |
| MSC: | 13D45 |
| MSC: | 13E05 |
| MSC: | 14B15 |
| idZBL: | Zbl 07547219 |
| idMR: | MR4412774 |
| DOI: | 10.21136/CMJ.2022.0050-21 |
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| Date available: | 2022-04-21T19:05:01Z |
| Last updated: | 2022-09-08 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150416 |
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