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

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Khashyarmanesh K., Yassi M., Abbasi A.

Colloquium Mathematicum

2004

tom 100

nr 2

213-219

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.

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1 Colloquium Mathematicum

1 Abbasi A.

1 Khashyarmanesh K.

1 Yassi M.

1 2004

Wyniki wyszukiwania

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