| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-04-21T19:05:01Z |
| Last updated:
|
2024-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150416 |
| . |
| Reference:
|
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