Top local cohomology and the catenaricity of the unmixed support of a finitely generated module
| dc.creator | Cuong, Nguyen Tu | |
| dc.creator | Dung, Nguyen Thi | |
| dc.creator | Nhan, Le Thanh | |
| dc.date | 2007-01-24 | |
| dc.date.accessioned | 2026-07-07T07:42:50Z | |
| dc.date.available | 2026-07-07T07:42:50Z | |
| dc.description | Let $(R,\m)$ be a Noetherian local ring and $M$ a finitely generated $R-$module with $\dim M=d.$ This paper is concerned with the following property for the top local cohomology module $H^d_\m(M)$: $$\Ann (0:_{H^d_\m(M)}\p)=\p\ \text{for all prime ideals} \p\supseteq\Ann H^d_\m(M).$$ In this paper we will show that this property is equivalent to the catenaricity of the unmixed support $\Usupp M$ of $M$ which is defined by $\Usupp M=\Supp M/U_M(0)$, where $U_M(0)$ is the largest submodule of $M$ of dimension less than $d.$ Some characterizations of this property in terms of system of parameters as well as the relation between the unmixed supports of $M$ and of the $\m$-adic completion $\hat M$ are given. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701675 | |
| dc.identifier | http://arxiv.org/abs/math/0701675 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122593 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D45; 13E10 | |
| dc.title | Top local cohomology and the catenaricity of the unmixed support of a finitely generated module | |
| dc.type | text |