| Title:
|
Annihilators of local homology modules (English) |
| Author:
|
Rezaei, Shahram |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
225-234 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(R,{\mathfrak m})$ be a local ring, $\mathfrak a$ an ideal of $R$ and $M$ a nonzero Artinian $R$-module of Noetherian dimension $n$ with ${\rm hd}(\mathfrak a, M)=n $. We determine the annihilator of the top local homology module ${\rm H}_{n}^{\mathfrak a}(M)$. In fact, we prove that $$ {\rm Ann}_R({\rm H}_{n}^{\mathfrak a}(M))={\rm Ann}_R(N(\frak a,M)), $$ where $N(\mathfrak a,M)$ denotes the smallest submodule of $M$ such that ${\rm hd}({\mathfrak a},M/N(\frak a,M))<n$. As a consequence, it follows that for a complete local ring $(R,\mathfrak m)$ all associated primes of ${\rm H}_{n}^{\mathfrak a}(M) $ are minimal. (English) |
| Keyword:
|
local homology |
| Keyword:
|
Artinian modules |
| Keyword:
|
annihilator |
| MSC:
|
13D45 |
| MSC:
|
13E05 |
| idZBL:
|
Zbl 07088781 |
| idMR:
|
MR3923586 |
| DOI:
|
10.21136/CMJ.2018.0263-17 |
| . |
| Date available:
|
2019-03-08T15:00:53Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147629 |
| . |
| Reference:
|
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| . |
