Some results on the annihilators and attached primes of local cohomology modules

Atazadeh, Ali; Sedghi, Monireh; Naghipour, Reza

doi:10.1007/s00013-017-1081-9

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2020

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Cited by 5 publications

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“…(vi) In this case, by [1, Theorem 2.8], H j a (N ) is a-cofinite minimax for all j < c. Therefore [12, Theorem 2.2] implies that (0 : , proved the cases cd(a, N ) = 1 and (iv) in above corollary when R is local. See also [4,Lemma 2.15 ] for the case cd(a, N ) = 0.…”

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confidence: 99%

Annihilator of Top Local Cohomology and Lynch's Conjecture

Fathi¹

2022

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Let R be a commutative Noetherian ring, a a proper ideal of R and N a nonzero finitely generated R-module with N = aN . Let c be the greatest nonnegative integer i such that the local cohomology H i a (N ) is nonzero. In this paper, we provide a sharp bound under inclusion for the annihilator of the top local cohomology module H c a (N ) and this annihilator is computed in certain cases. Also, using this bound, we construct a counterexample to Lynch's conjecture.

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confidence: 99%