| Title:
|
Some results on the local cohomology of minimax modules (English) |
| Author:
|
Abbasi, Ahmad |
| Author:
|
Roshan-Shekalgourabi, Hajar |
| Author:
|
Hassanzadeh-Lelekaami, Dawood |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
327-333 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative Noetherian ring with identity and $I$ an ideal of $R$. It is shown that, if $M$ is a non-zero minimax $R$-module such that $\dim \mathop {\rm Supp} H^i_I (M) \leq 1$ for all $i$, then the $R$-module $H^i_I(M)$ is $I$-cominimax for all $i$. In fact, $H^i_I(M)$ is $I$-cofinite for all $i\geq 1$. Also, we prove that for a weakly Laskerian $R$-module $M$, if $R$ is local and $t$ is a non-negative integer such that $\dim \mathop {\rm Supp} H^i_I (M)\leq 2$ for all $i<t$, then ${\rm Ext}^j_R (R/I, H^i_I (M))$ and ${\rm Hom}_R(R/I, H^t_I(M))$ are weakly Laskerian for all $i<t$ and all $j \geq 0$. As a consequence, the set of associated primes of $H^i_I (M)$ is finite for all $i\geq 0$, whenever $\dim R/I \leq 2$ and $M$ is weakly Laskerian. (English) |
| Keyword:
|
local cohomology module |
| Keyword:
|
Krull dimension |
| Keyword:
|
minimax module |
| Keyword:
|
cofinite module |
| Keyword:
|
weakly Laskerian module |
| Keyword:
|
associated primes |
| MSC:
|
13C05 |
| MSC:
|
13D45 |
| MSC:
|
13E10 |
| idZBL:
|
Zbl 06391497 |
| idMR:
|
MR3277739 |
| DOI:
|
10.1007/s10587-014-0104-y |
| . |
| Date available:
|
2014-11-10T09:31:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144001 |
| . |
| Reference:
|
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