Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 2, pp. 541-558, 2022

Local cohomology, cofiniteness and homological functors of modules

Kamal Bahmanpour

Received February 9, 2021. Published online January 14, 2022.

Abstract: 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 $i,j\in\Bbb{N}_0$.

Keywords: cofinite module; cohomological dimension; ideal transform; local cohomology; Noetherian ring

Classification MSC: 13D45, 14B15, 13E05

DOI: 10.21136/CMJ.2022.0050-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Kamal Bahmanpour, Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Daneshgah Street, Ardabil, 56199-11367, Iran, e-mail: bahmanpour.k@gmail.com

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