Cohomological dimension filtration and annihilators of top local cohomology modules

Ali Atazadeh, Monireh Sedghi, and Reza Naghipour. "Cohomological dimension filtration and annihilators of top local cohomology modules." Colloquium Mathematicae 139.1 (2015): 25-35. <http://eudml.org/doc/284334>.

@article{AliAtazadeh2015,
abstract = {Let denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration $ = \{M_i\}_\{i = 0\}^\{c\}$, where c = cd(,M) and $M_i$ denotes the largest submodule of M such that $cd(,M_i) ≤ i$. Some properties of this filtration are investigated. In particular, if (R,) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module $H_\{\}^\{c\}(M)$, namely $Ann_\{R\}(H_\{\}^\{c\}(M)) = Ann_\{R\}(M/M_\{c-1\})$. As a consequence, there exists an ideal of R such that $Ann_\{R\}(H_\{\}^\{c\}(M)) = Ann_\{R\}(M/H⁰_\{\}(M))$. This generalizes the main results of Bahmanpour et al. (2012) and Lynch (2012).},
author = {Ali Atazadeh, Monireh Sedghi, Reza Naghipour},
journal = {Colloquium Mathematicae},
keywords = {annihilator; attached primes; cohomological dimension; local cohomology},
language = {eng},
number = {1},
pages = {25-35},
title = {Cohomological dimension filtration and annihilators of top local cohomology modules},
url = {http://eudml.org/doc/284334},
volume = {139},
year = {2015},
}

TY - JOUR
AU - Ali Atazadeh
AU - Monireh Sedghi
AU - Reza Naghipour
TI - Cohomological dimension filtration and annihilators of top local cohomology modules
JO - Colloquium Mathematicae
PY - 2015
VL - 139
IS - 1
SP - 25
EP - 35
AB - Let denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration $ = {M_i}_{i = 0}^{c}$, where c = cd(,M) and $M_i$ denotes the largest submodule of M such that $cd(,M_i) ≤ i$. Some properties of this filtration are investigated. In particular, if (R,) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module $H_{}^{c}(M)$, namely $Ann_{R}(H_{}^{c}(M)) = Ann_{R}(M/M_{c-1})$. As a consequence, there exists an ideal of R such that $Ann_{R}(H_{}^{c}(M)) = Ann_{R}(M/H⁰_{}(M))$. This generalizes the main results of Bahmanpour et al. (2012) and Lynch (2012).
LA - eng
KW - annihilator; attached primes; cohomological dimension; local cohomology
UR - http://eudml.org/doc/284334
ER -