Reducing system of parameters and the Cohen--Macaulay property
| dc.creator | Maurer, Bjorn | |
| dc.creator | Stuckrad, Jurgen | |
| dc.date | 2007-07-14 | |
| dc.date.accessioned | 2026-07-07T08:18:25Z | |
| dc.date.available | 2026-07-07T08:18:25Z | |
| dc.description | Let $R$ be a local ring and let ($x_1\biss x_r$) be part of a system of parameters of a finitely generated $R$-module $M,$ where $r < \dim_R M$. We will show that if ($y_1\biss y_r$) is part of a reducing system of parameters of $M$ with $(y_1\biss y_r)M=(x_1\biss x_r)M$ then $(x_1\biss x_r)$ is already reducing. Moreover, there is such a part of a reducing system of parameters of $M$ iff for all primes $P\in \supp M \cap V_R(x_1\biss x_r)$ with $\dim_R R/P = \dim_R M -r$ the localization $M_P$ of $M$ at $P$ is an $r$-dimensional \cm\ module over $R_P$. Furthermore, we will show that $M$ is a \cm module iff $y_d$ is a non zero divisor on $M/(y_1\biss y_{d-1})M$, where $(y_1\biss y_d)$ is a reducing system of parameters of $M$ ($d := \dim_R M$). | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/0707.2136 | |
| dc.identifier | http://arxiv.org/abs/0707.2136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134422 | |
| dc.subject | Commutative Algebra | |
| dc.title | Reducing system of parameters and the Cohen--Macaulay property | |
| dc.type | text |