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

Abstract

top
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.

How to cite

top

Majd, 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},
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
UR - http://eudml.org/doc/276107
ER -

References

top
  1. 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) 
  2. 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
  3. Cuong, N. T., Cuong, D. T., 10.2996/kmj/1193924944, Kodai Math. J. 30 (2007), 409-428. (2007) Zbl1139.13011MR2372128DOI10.2996/kmj/1193924944
  4. 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
  5. Eisenbud, D., Commutative Algebra. With a View Toward Algebraic Geometry, Graduate Texts in Mathematics 150 Springer, Berlin (1995). (1995) Zbl0819.13001MR1322960
  6. Rahimi, A., Sequentially Cohen-Macaulayness of bigraded modules, (to appear) in Rocky Mt. J. Math. 
  7. Rahimi, A., 10.1016/j.jalgebra.2009.11.026, J. Algebra 323 (2010), 1745-1757. (2010) Zbl1184.13053MR2588136DOI10.1016/j.jalgebra.2009.11.026
  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. (1999) Zbl0942.13015MR1702109

NotesEmbed ?

top

You must be logged in to post comments.