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

• Autorzy: K. Khashyarmanesh , M. Yassi , A. Abbasi
• Języki publikacji: EN

Abstrakty

EN

Let R be a commutative Noetherian ring. Let 𝔞 and 𝔟 be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the 𝔟-finiteness dimension of $f^{𝔟}_{𝔞}(N)$ relative to 𝔞 in the context of generalized local cohomology modules as
$f^{𝔟}_{𝔞}(M,N): = inf{i ≥ 0 | 𝔟 ⊆ √(0:_R H^{i}_{𝔞}(M,N))}$,
where M is an R-module. We also show that $f^{𝔟}_{𝔞}(N) ≤ f^{𝔟}_{𝔞}(M,N)$ 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.

Kategorie tematyczne

• 13D45: Local cohomology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 100
• Numer: 2
• Strony: 213-219

Daty

wydano

2004

Twórcy

autor

K. Khashyarmanesh

• Institute for Studies in, Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran

autor

M. Yassi

• Department of Mathematics, Mashhad University, P.O. Box 1159-91775, Mashhad, Iran

autor

A. Abbasi

• Department of Mathematics, Mashhad University, P.O. Box 1159-91775, Mashhad, Iran

Identyfikatory

DOI

10.4064/cm100-2-5