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1

On the uniform behaviour of the Frobenius closures of ideals

100%

Khashyarmanesh K.

Colloquium Mathematicum

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2007

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tom 109

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nr 1

1-7

EN

Let 𝔞 be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q(𝔞) be the smallest positive integer m such that $(𝔞^{F})^{[p^m]} = 𝔞^{[p^m]}$, where $𝔞^{F}$ is the Frobenius closure of 𝔞. This paper is concerned with the question whether the set ${Q(𝔞^{[p^m]}) : m ∈ ℕ₀}$ is bounded. We give an affirmative answer in the case that the ideal 𝔞 is generated by an u.s.d-sequence c₁,..., cₙ for R such that (i) the map $R/∑_{j=1}^{n} Rc_j → R/∑_{j = 1}^{n} Rc²_j$ induced by multiplication by c₁...cₙ is an R-monomorphism; (ii) for all $𝔭 ∈ ass(c₁^j, ..., cₙ^j)$, c₁/1,..., cₙ/1 is a $𝔭R_{𝔭}$-filter regular sequence for $R_{𝔭}$ for j ∈ {1,2}.

2

General local cohomology modules and Koszul homology modules

63%

Khashyarmanesh K., Salarian S.

Colloquium Mathematicum

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1998

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tom 77

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nr 2

305-313

3

Local-global principle for annihilation of general local cohomology

51%

Asadollahi J., Khashyarmanesh K., Salarian S.

Colloquium Mathematicum

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2001

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tom 87

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nr 1

129-136

EN

Let A be a Noetherian ring, let M be a finitely generated A-module and let Φ be a system of ideals of A. We prove that, for any ideal 𝔞 in Φ, if, for every prime ideal 𝔭 of A, there exists an integer k(𝔭), depending on 𝔭, such that $𝔞^{k(𝔭)}$ kills the general local cohomology module $H_{Φ_{𝔭}}^{j}(M_{𝔭})$ for every integer j less than a fixed integer n, where $Φ_{𝔭}: = {𝔞_{𝔭}: 𝔞 ∈ Φ}$, then there exists an integer k such that $𝔞^{k}H_{Φ}^{j}(M) = 0$ for every j < n.

4

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

51%

Khashyarmanesh K., Yassi M., Abbasi A.

Colloquium Mathematicum

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2004

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tom 100

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nr 2

213-219

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.

Ograniczanie wyników

4 Colloquium Mathematicum

4 Khashyarmanesh K.

2 Salarian S.

1 Abbasi A.

1 Asadollahi J.

1 Yassi M.

1 2007

1 2004

1 2001

1 1998

On the uniform behaviour of the Frobenius closures of ideals

General local cohomology modules and Koszul homology modules

Local-global principle for annihilation of general local cohomology

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