| Title:
|
Pretty cleanness and filter-regular sequences (English) |
| Author:
|
Bandari, Somayeh |
| Author:
|
Divaani-Aazar, Kamran |
| Author:
|
Jahan, Ali Soleyman |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
933-944 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $K$ be a field and $S=K[x_1,\ldots , x_n]$. Let $I$ be a monomial ideal of $S$ and $u_1,\ldots , u_r$ be monomials in $S$. We prove that if $u_1,\ldots , u_r$ form a filter-regular sequence on $S/I$, then $S/I$ is pretty clean if and only if $S/(I,u_1,\ldots , u_r)$ is pretty clean. Also, we show that if $u_1,\ldots , u_r$ form a filter-regular sequence on $S/I$, then Stanley's conjecture is true for $S/I$ if and only if it is true for $S/(I,u_1, \ldots , u_r)$. Finally, we prove that if $u_1,\ldots , u_r$ is a minimal set of generators for $I$ which form either a $d$-sequence, proper sequence or strong $s$-sequence (with respect to the reverse lexicographic order), then $S/I$ is pretty clean. (English) |
| Keyword:
|
almost clean module |
| Keyword:
|
clean module |
| Keyword:
|
$d$-sequence |
| Keyword:
|
filter-regular sequence |
| Keyword:
|
pretty clean module |
| MSC:
|
05E40 |
| MSC:
|
13F20 |
| idZBL:
|
Zbl 06433705 |
| idMR:
|
MR3304789 |
| DOI:
|
10.1007/s10587-014-0144-3 |
| . |
| Date available:
|
2015-02-09T17:27:32Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144152 |
| . |
| Reference:
|
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