| Title:
|
On the structure of sequentially Cohen-Macaulay bigraded modules (English) |
| Author:
|
Majd, Leila Parsaei |
| Author:
|
Rahimi, Ahad |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
1011-1022 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $K$ be a field and $S=K[x_1,\ldots ,x_m, y_1,\ldots ,y_n]$ be the standard bigraded polynomial ring over $K$. In this paper, we explicitly describe the structure of finitely generated bigraded ``sequentially Cohen-Macaulay'' $S$-modules with respect to $Q=(y_1,\ldots ,y_n)$. Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to $Q$ in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to $Q$ are considered. (English) |
| Keyword:
|
dimension filtration |
| Keyword:
|
sequentially Cohen-Macaulay filtration |
| Keyword:
|
cohomological dimension |
| Keyword:
|
bigraded module |
| Keyword:
|
Cohen-Macaulay module |
| MSC:
|
13C14 |
| MSC:
|
13D45 |
| MSC:
|
16W50 |
| MSC:
|
16W70 |
| idZBL:
|
Zbl 06537707 |
| idMR:
|
MR3441332 |
| DOI:
|
10.1007/s10587-015-0224-z |
| . |
| Date available:
|
2016-01-13T09:15:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144789 |
| . |
| Reference:
|
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| Reference:
|
[2] Chardin, M., Jouanolou, J.-P., Rahimi, A.: The eventual stability of depth, associated primes and cohomology of a graded module.J. Commut. Algebra 5 (2013), 63-92. Zbl 1275.13014, MR 3084122, 10.1216/JCA-2013-5-1-63 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[6] Rahimi, A.: Sequentially Cohen-Macaulayness of bigraded modules.(to appear) in Rocky Mt. J. Math. |
| Reference:
|
[7] Rahimi, A.: Relative Cohen-Macaulayness of bigraded modules.J. Algebra 323 (2010), 1745-1757. Zbl 1184.13053, MR 2588136, 10.1016/j.jalgebra.2009.11.026 |
| Reference:
|
[8] Schenzel, P.: On the dimension filtration and Cohen-Macaulay filtered modules.Commutative Algebra and Algebraic Geometry. Proc. of the Ferrara Meeting, Italy F. Van Oystaeyen Lecture Notes Pure Appl. Math. 206 Marcel Dekker, New York (1999), 245-264. Zbl 0942.13015, MR 1702109 |
| . |
