# Cohomological dimension filtration and annihilators of top local cohomology modules

Ali Atazadeh; Monireh Sedghi; Reza Naghipour

Colloquium Mathematicae (2015)

- Volume: 139, Issue: 1, page 25-35
- ISSN: 0010-1354

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topAli 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 -

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