A new version of Local-Global Principle for annihilations of local cohomology modules

K. Khashyarmanesh; M. Yassi; A. Abbasi

Colloquium Mathematicae (2004)

  • Volume: 100, Issue: 2, page 213-219
  • ISSN: 0010-1354

Abstract

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Let R be a commutative Noetherian ring. Let and be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the -finiteness dimension of f ( N ) relative to in the context of generalized local cohomology modules as f ( M , N ) : = i n f i ≥ 0 | ⊆ √ ( 0 : R H i ( M , N ) ) , where M is an R-module. We also show that f ( N ) ≤ f ( M , N ) for any R-module M. This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.

How to cite

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K. Khashyarmanesh, M. Yassi, and A. Abbasi. "A new version of Local-Global Principle for annihilations of local cohomology modules." Colloquium Mathematicae 100.2 (2004): 213-219. <http://eudml.org/doc/284367>.

@article{K2004,
abstract = {Let R be a commutative Noetherian ring. Let and be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the -finiteness dimension of $f^\{\}_\{\}(N)$ relative to in the context of generalized local cohomology modules as $f^\{\}_\{\}(M,N): = inf\{i ≥ 0 | ⊆ √(0:_R H^\{i\}_\{\}(M,N))\}$, where M is an R-module. We also show that $f^\{\}_\{\}(N) ≤ f^\{\}_\{\}(M,N)$ for any R-module M. This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.},
author = {K. Khashyarmanesh, M. Yassi, A. Abbasi},
journal = {Colloquium Mathematicae},
keywords = {finiteness dimension; generalized local cohomology},
language = {eng},
number = {2},
pages = {213-219},
title = {A new version of Local-Global Principle for annihilations of local cohomology modules},
url = {http://eudml.org/doc/284367},
volume = {100},
year = {2004},
}

TY - JOUR
AU - K. Khashyarmanesh
AU - M. Yassi
AU - A. Abbasi
TI - A new version of Local-Global Principle for annihilations of local cohomology modules
JO - Colloquium Mathematicae
PY - 2004
VL - 100
IS - 2
SP - 213
EP - 219
AB - Let R be a commutative Noetherian ring. Let and be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the -finiteness dimension of $f^{}_{}(N)$ relative to in the context of generalized local cohomology modules as $f^{}_{}(M,N): = inf{i ≥ 0 | ⊆ √(0:_R H^{i}_{}(M,N))}$, where M is an R-module. We also show that $f^{}_{}(N) ≤ f^{}_{}(M,N)$ for any R-module M. This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.
LA - eng
KW - finiteness dimension; generalized local cohomology
UR - http://eudml.org/doc/284367
ER -

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