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Cohomological dimension filtration and annihilators of top local cohomology modules

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Atazadeh A., Sedghi M., Naghipour R.

Colloquium Mathematicum

2015

tom 139

nr 1

25-35

Let 𝔞 denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration $𝓜 = {M_i}_{i = 0}^{c}$, where c = cd(𝔞,M) and $M_i$ denotes the largest submodule of M such that $cd(𝔞,M_i) ≤ i$. Some properties of this filtration are investigated. In particular, if (R,𝔪) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module $H_{𝔞}^{c}(M)$, namely $Ann_{R}(H_{𝔞}^{c}(M)) = Ann_{R}(M/M_{c-1})$. As a consequence, there exists an ideal 𝔟 of R such that $Ann_{R}(H_{𝔞}^{c}(M)) = Ann_{R}(M/H⁰_{𝔟}(M))$. This generalizes the main results of Bahmanpour et al. (2012) and Lynch (2012).

Ograniczanie wyników

1 Colloquium Mathematicum

1 Atazadeh A.

1 Naghipour R.

1 Sedghi M.

1 2015

Wyniki wyszukiwania

Cohomological dimension filtration and annihilators of top local cohomology modules