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Local cohomology, cofiniteness and homological functors of modules
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 541-558
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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 $i,j\in \Bbb {N}_0$.
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 $i,j\in \Bbb {N}_0$.
DOI : 10.21136/CMJ.2022.0050-21
Classification : 13D45, 13E05, 14B15
Keywords: cofinite module; cohomological dimension; ideal transform; local cohomology; Noetherian ring 
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Bahmanpour, Kamal. Local cohomology, cofiniteness and homological functors of modules. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 541-558. doi: 10.21136/CMJ.2022.0050-21

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