Cohomological dimension filtration and annihilators of top local cohomology modules

• Autorzy: Ali Atazadeh , Monireh Sedghi , Reza Naghipour
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 14B15: Local cohomology
• 13E05: Noetherian rings and modules
• 13D45: Local cohomology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 139
• Numer: 1
• Strony: 25-35

Daty

wydano

2015

Twórcy

autor

Ali Atazadeh

• Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

autor

Monireh Sedghi

• Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

autor

Reza Naghipour

• Department of Mathematics, University of Tabriz, Tabriz, Iran

Identyfikatory

DOI

10.4064/cm139-1-2