# Article

Full entry | Fulltext not available (moving wall 24 months)
Keywords:
dimension filtration; sequentially Cohen-Macaulay filtration; cohomological dimension; bigraded module; Cohen-Macaulay module
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.
References:
[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.
[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. DOI 10.1216/JCA-2013-5-1-63 | MR 3084122 | Zbl 1275.13014
[3] Cuong, N. T., Cuong, D. T.: On sequentially Cohen-Macaulay modules. Kodai Math. J. 30 (2007), 409-428. DOI 10.2996/kmj/1193924944 | MR 2372128 | Zbl 1139.13011
[4] Cuong, N. T., Cuong, D. T.: On the structure of sequentially generalized Cohen-Macaulay modules. J. Algebra 317 (2007), 714-742. DOI 10.1016/j.jalgebra.2007.06.026 | MR 2362938 | Zbl 1137.13010
[5] Eisenbud, D.: Commutative Algebra. With a View Toward Algebraic Geometry. Graduate Texts in Mathematics 150 Springer, Berlin (1995). MR 1322960 | Zbl 0819.13001
[6] Rahimi, A.: Sequentially Cohen-Macaulayness of bigraded modules. (to appear) in Rocky Mt. J. Math.
[7] Rahimi, A.: Relative Cohen-Macaulayness of bigraded modules. J. Algebra 323 (2010), 1745-1757. DOI 10.1016/j.jalgebra.2009.11.026 | MR 2588136 | Zbl 1184.13053
[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. MR 1702109 | Zbl 0942.13015

Partner of