Cohomological dimension filtration and annihilators of top local cohomology modules

Ali Atazadeh; Monireh Sedghi; Reza Naghipour

Ali Atazadeh ; Monireh Sedghi ; Reza Naghipour

Colloquium Mathematicae, Tome 139 (2015), p. 25-35 / Harvested from The Polish Digital Mathematics Library

Résumé

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

Publié le : 2015-01-01

Zbl 1314.13033

EUDML-ID : urn:eudml:doc:284334

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     title = {Cohomological dimension filtration and annihilators of top local cohomology modules},
     journal = {Colloquium Mathematicae},
     volume = {139},
     year = {2015},
     pages = {25-35},
     zbl = {1314.13033},
     language = {en},
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Ali Atazadeh; Monireh Sedghi; Reza Naghipour. Cohomological dimension filtration and annihilators of top local cohomology modules. Colloquium Mathematicae, Tome 139 (2015) pp. 25-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-1-2/