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Quintasymptotic primes, local cohomology and ideal topologies

A. A. MehrvarzR. NaghipourM. Sedghi — 2006

Colloquium Mathematicae

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...

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