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 and 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 , 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 -topology.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-3,
author = {A. A. Mehrvarz and R. Naghipour and M. Sedghi},
title = {Quintasymptotic primes, local cohomology and ideal topologies},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {25-37},
zbl = {1101.13027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-3}
}
A. A. Mehrvarz; R. Naghipour; M. Sedghi. Quintasymptotic primes, local cohomology and ideal topologies. Colloquium Mathematicae, Tome 106 (2006) pp. 25-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-3/