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2019 Cohomological dimension and top local cohomology modules
Vahap Erdoğdu, Tuğba Yıldırım
Rocky Mountain J. Math. 49(6): 1843-1855 (2019). DOI: 10.1216/RMJ-2019-49-6-1843

Abstract

Let $R$ be a Noetherian ring, $I$ an ideal of $R$ and $M$ an $R$-module. In this paper, we first determine a condition under which a given integer $t$ is a lower bound for the cohomological dimension $\operatorname {cd}(I,M)$, and use this to conclude that non-catenary Noetherian domains contain prime ideals that are not set-theoretic complete intersection. We also show the existence of a descending chain of ideals with successive diminishing cohomological dimensions. We then resolve the Artinianness of top local cohomology modules over local unique factorization domains of Krull dimension at most three, and obtain several related results on the top local cohomology modules for much more general cases.

Citation

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Vahap Erdoğdu. Tuğba Yıldırım. "Cohomological dimension and top local cohomology modules." Rocky Mountain J. Math. 49 (6) 1843 - 1855, 2019. https://doi.org/10.1216/RMJ-2019-49-6-1843

Information

Published: 2019
First available in Project Euclid: 3 November 2019

zbMATH: 07136581
MathSciNet: MR4027236
Digital Object Identifier: 10.1216/RMJ-2019-49-6-1843

Subjects:
Primary: 13D45
Secondary: 13E10

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 6 • 2019
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