Parametric Decomposition of Powers of Parameter Ideals and Sequentially Cohen-Macaulay Modules
| dc.creator | Cuong, Nguyen Tu | |
| dc.creator | Truong, Hoang Le | |
| dc.date | 2007-01-25 | |
| dc.date.accessioned | 2026-07-07T07:43:01Z | |
| dc.date.available | 2026-07-07T07:43:01Z | |
| dc.description | Let $M$ be a finitely generated module of dimension $d$ over a Noetherian local ring $(R,\m)$ and $\q $ the parameter ideal generated by a system of parameters $\x = (x_1,..., x_d)$ of $M$. For each positive integer $n$, set $$Λ_{d,n}=\{α=(α_1,...,α_d)\in\Bbb{Z}^d|α_i\geqslant 1, \forall 1\leqslant i\leqslant d \text{and} \sum\limits_{i=1}^dα_i=d+n-1\}$$ and $\qa = (x_1^{α_1},...,x_d^{α_d})$. Then we prove in this note that $M$ is a sequentially Cohen-Macaulay module if and only if there exists a certain system of parameters $\x$ such that the equality $\q^nM=\pd$ holds true for all $n$. As an application of this result, we can compute the Hilbert-Samuel polynomial of a sequentially Cohen-Macaulay module with respect to certain parameter ideals | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701730 | |
| dc.identifier | http://arxiv.org/abs/math/0701730 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122664 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13H99, 13H10 | |
| dc.title | Parametric Decomposition of Powers of Parameter Ideals and Sequentially Cohen-Macaulay Modules | |
| dc.type | text |