| Title:
|
The strong persistence property and symbolic strong persistence property (English) |
| Author:
|
Nasernejad, Mehrdad |
| Author:
|
Khashyarmanesh, Kazem |
| Author:
|
Roberts, Leslie G. |
| Author:
|
Toledo, Jonathan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
209-237 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $I$ be an ideal in a commutative Noetherian ring $R$. Then the ideal $I$ has the strong persistence property if and only if $(I^{k+1}\colon _R I)=I^k$ for all $k$, and $I$ has the symbolic strong persistence property if and only if $(I^{(k+1)}\colon _R I^{(1)})=I^{(k)}$ for all $k$, where $I^{(k)}$ denotes the $k$th symbolic power of $I$. We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial ideal has the symbolic strong persistence property. (English) |
| Keyword:
|
strong persistence property |
| Keyword:
|
associated prime |
| Keyword:
|
cover ideal |
| Keyword:
|
symbolic strong persistence property |
| MSC:
|
05C25 |
| MSC:
|
05E40 |
| MSC:
|
13A30 |
| MSC:
|
13B25 |
| MSC:
|
13C13 |
| MSC:
|
13P25 |
| idZBL:
|
Zbl 07511563 |
| idMR:
|
MR4389116 |
| DOI:
|
10.21136/CMJ.2021.0407-20 |
| . |
| Date available:
|
2022-03-25T08:30:59Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149583 |
| . |
| Reference:
|
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