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Title: Local cohomology, cofiniteness and homological functors of modules (English)
Author: Bahmanpour, Kamal
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 72
Issue: 2
Year: 2022
Pages: 541-558
Summary lang: English
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Category: math
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Summary: Let $I$ be an ideal of a commutative Noetherian ring $R$. It is shown that the $R$-modules $H^j_I(M)$ are $I$-cofinite for all finitely generated $R$-modules $M$ and all $j\in \Bbb {N}_0$ if and only if the $R$-modules ${\rm Ext}^i_R(N,H^j_I(M))$ and ${\rm Tor}^R_i(N,H^j_I(M))$ are $I$-cofinite for all finitely generated $R$-modules $M$, $N$ and all integers $i,j\in \Bbb {N}_0$. (English)
Keyword: cofinite module
Keyword: cohomological dimension
Keyword: ideal transform
Keyword: local cohomology
Keyword: Noetherian ring
MSC: 13D45
MSC: 13E05
MSC: 14B15
idZBL: Zbl 07547219
idMR: MR4412774
DOI: 10.21136/CMJ.2022.0050-21
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Date available: 2022-04-21T19:05:01Z
Last updated: 2024-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/150416
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