Quintasymptotic primes, local cohomology and ideal topologies

• Autorzy: A. A. Mehrvarz , R. Naghipour , M. Sedghi
• Języki publikacji: EN

Abstrakty

EN

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,𝔪) 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 ∩ 𝔪 ≠ ∅ and the S(Φ)-topology is finer than the $Φ_{a}$-topology.

Kategorie tematyczne

• 13E05: Noetherian rings and modules
• 13D45: Local cohomology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 1
• Strony: 25-37

Daty

wydano

2006

Twórcy

autor

A. A. Mehrvarz

• Department of Mathematics, University of Tabriz, Tabriz, Iran

autor

R. Naghipour

• Department of Mathematics, University of Tabriz, Tabriz, Iran

autor

M. Sedghi

• Department of Mathematics, Azarbaidjan University of Tarbiat Moallem, Azarshahr, Tabriz, Iran

Identyfikatory

DOI

10.4064/cm106-1-3