On the structure of sequentially Cohen-Macaulay bigraded modules
Leila Parsaei Majd; Ahad Rahimi
Czechoslovak Mathematical Journal (2015)
- Volume: 65, Issue: 4, page 1011-1022
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topMajd, Leila Parsaei, and Rahimi, Ahad. "On the structure of sequentially Cohen-Macaulay bigraded modules." Czechoslovak Mathematical Journal 65.4 (2015): 1011-1022. <http://eudml.org/doc/276107>.
@article{Majd2015,
abstract = {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.},
author = {Majd, Leila Parsaei, Rahimi, Ahad},
journal = {Czechoslovak Mathematical Journal},
keywords = {dimension filtration; sequentially Cohen-Macaulay filtration; cohomological dimension; bigraded module; Cohen-Macaulay module},
language = {eng},
number = {4},
pages = {1011-1022},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the structure of sequentially Cohen-Macaulay bigraded modules},
url = {http://eudml.org/doc/276107},
volume = {65},
year = {2015},
}
TY - JOUR
AU - Majd, Leila Parsaei
AU - Rahimi, Ahad
TI - On the structure of sequentially Cohen-Macaulay bigraded modules
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 1011
EP - 1022
AB - 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.
LA - eng
KW - dimension filtration; sequentially Cohen-Macaulay filtration; cohomological dimension; bigraded module; Cohen-Macaulay module
UR - http://eudml.org/doc/276107
ER -
References
top- Capani, A., Niesi, G., Robbiano, L., CoCoA, a system for doing Computations in Commutative Algebra, (1995), http://cocoa.dima.unige.it./research/publications.html, 1995. (1995)
- Chardin, M., Jouanolou, J.-P., Rahimi, A., 10.1216/JCA-2013-5-1-63, J. Commut. Algebra 5 (2013), 63-92. (2013) Zbl1275.13014MR3084122DOI10.1216/JCA-2013-5-1-63
- Cuong, N. T., Cuong, D. T., 10.2996/kmj/1193924944, Kodai Math. J. 30 (2007), 409-428. (2007) Zbl1139.13011MR2372128DOI10.2996/kmj/1193924944
- Cuong, N. T., Cuong, D. T., 10.1016/j.jalgebra.2007.06.026, J. Algebra 317 (2007), 714-742. (2007) Zbl1137.13010MR2362938DOI10.1016/j.jalgebra.2007.06.026
- Eisenbud, D., Commutative Algebra. With a View Toward Algebraic Geometry, Graduate Texts in Mathematics 150 Springer, Berlin (1995). (1995) Zbl0819.13001MR1322960
- Rahimi, A., Sequentially Cohen-Macaulayness of bigraded modules, (to appear) in Rocky Mt. J. Math.
- Rahimi, A., 10.1016/j.jalgebra.2009.11.026, J. Algebra 323 (2010), 1745-1757. (2010) Zbl1184.13053MR2588136DOI10.1016/j.jalgebra.2009.11.026
- 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. (1999) Zbl0942.13015MR1702109
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.