CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Faltings' Finiteness Dimension of Local Cohomology Modules Over Local Cohen-Macaulay Rings

  Published:2017-02-16
 Printed: Jun 2017
  • Kamal Bahmanpour,
    Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran
  • Reza Naghipour,
    Department of Mathematics, University of Tabriz, Tabriz, Iran
Format:   LaTeX   MathJax   PDF  

Abstract

Let $(R, \frak m)$ denote a local Cohen-Macaulay ring and $I$ a non-nilpotent ideal of $R$. The purpose of this article is to investigate Faltings' finiteness dimension $f_I(R)$ and equidimensionalness of certain homomorphic image of $R$. As a consequence we deduce that $f_I(R)=\operatorname{max}\{1, \operatorname{ht} I\}$ and if $\operatorname{mAss}_R(R/I)$ is contained in $\operatorname{Ass}_R(R)$, then the ring $R/ I+\cup_{n\geq 1}(0:_RI^n)$ is equidimensional of dimension $\dim R-1$. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module $H^{\operatorname{ht} I}_I(R)$, in the case $(R, \frak m)$ is a complete equidimensional local ring.
Keywords: Cohen Macaulay ring, equidimensional ring, finiteness dimension, local cohomology Cohen Macaulay ring, equidimensional ring, finiteness dimension, local cohomology
MSC Classifications: 13D45, 14B15 show english descriptions Local cohomology [See also 14B15]
Local cohomology [See also 13D45, 32C36]
13D45 - Local cohomology [See also 14B15]
14B15 - Local cohomology [See also 13D45, 32C36]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/