| Title:
|
Cominimaxness of local cohomology modules (English) |
| Author:
|
Aghapournahr, Moharram |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
75-86 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$. Let $t\in \mathbb {N}_0$ be an integer and $M$ an $R$-module such that ${\rm Ext}^i_R(R/I,M)$ is minimax for all $i\leq t+1$. We prove that if $H^{i}_{I}(M)$ is ${\rm FD}_{\leq 1}$ (or weakly Laskerian) for all $i<t$, then the $R$-modules $H^{i}_{I}(M)$ are $I$-cominimax for all $i<t$ and ${\rm Ext}^i_R(R/I,H^{t}_{I}(M))$ is minimax for $i=0,1$. Let $N$ be a finitely generated $R$-module. We prove that ${\rm Ext}^j_R(N,H^{i}_{I}(M))$ and ${\rm Tor}^R_{j}(N,H^{i}_I(M))$ are $I$-cominimax for all $i$ and $j$ whenever $M$ is minimax and $H^{i}_{I}(M)$ is ${\rm FD}_{\leq 1}$ (or weakly Laskerian) for all $i$. (English) |
| Keyword:
|
local cohomology |
| Keyword:
|
${\rm FD}_{\leq n}$ modules |
| Keyword:
|
cofinite modules |
| Keyword:
|
cominimax modules |
| MSC:
|
13C05 |
| MSC:
|
13D45 |
| MSC:
|
13E10 |
| idZBL:
|
Zbl 07088770 |
| idMR:
|
MR3923575 |
| DOI:
|
10.21136/CMJ.2018.0161-17 |
| . |
| Date available:
|
2019-03-08T14:56:06Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147618 |
| . |
| Reference:
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| . |
