Quintasymptotic primes, local cohomology and ideal topologies

A. A. Mehrvarz; R. Naghipour; M. Sedghi

Colloquium Mathematicae (2006)

  • Volume: 106, Issue: 1, page 25-37
  • ISSN: 0010-1354

Abstract

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Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by I a I ∈ Φ and S ( I a ) I ∈ Φ are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then H Φ d ( R ) , the dth local cohomology module of R with respect to Φ, vanishes if and only if there exists a multiplicatively closed subset S of R such that S ∩ ≠ ∅ and the S(Φ)-topology is finer than the Φ a -topology.

How to cite

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A. A. Mehrvarz, R. Naghipour, and M. Sedghi. "Quintasymptotic primes, local cohomology and ideal topologies." Colloquium Mathematicae 106.1 (2006): 25-37. <http://eudml.org/doc/284348>.

@article{A2006,
abstract = {Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by $\{I_\{a\}\}_\{I∈Φ\}$ and $\{S(I_\{a\})\}_\{I∈Φ\}$ are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then $H^\{d\}_\{Φ\}(R)$, the dth local cohomology module of R with respect to Φ, vanishes if and only if there exists a multiplicatively closed subset S of R such that S ∩ ≠ ∅ and the S(Φ)-topology is finer than the $Φ_\{a\}$-topology.},
author = {A. A. Mehrvarz, R. Naghipour, M. Sedghi},
journal = {Colloquium Mathematicae},
keywords = {quintasymptotic primes; local cohomology; quasi-unmixed rings},
language = {eng},
number = {1},
pages = {25-37},
title = {Quintasymptotic primes, local cohomology and ideal topologies},
url = {http://eudml.org/doc/284348},
volume = {106},
year = {2006},
}

TY - JOUR
AU - A. A. Mehrvarz
AU - R. Naghipour
AU - M. Sedghi
TI - Quintasymptotic primes, local cohomology and ideal topologies
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 1
SP - 25
EP - 37
AB - Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by ${I_{a}}_{I∈Φ}$ and ${S(I_{a})}_{I∈Φ}$ are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then $H^{d}_{Φ}(R)$, the dth local cohomology module of R with respect to Φ, vanishes if and only if there exists a multiplicatively closed subset S of R such that S ∩ ≠ ∅ and the S(Φ)-topology is finer than the $Φ_{a}$-topology.
LA - eng
KW - quintasymptotic primes; local cohomology; quasi-unmixed rings
UR - http://eudml.org/doc/284348
ER -

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