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november 2020 On the cofiniteness of generalized local cohomology modules
Farzaneh Vahdanipour, Kamal Bahmanpour, Ghader Ghasemi
Bull. Belg. Math. Soc. Simon Stevin 27(4): 557-566 (november 2020). DOI: 10.36045/j.bbms.190211

Abstract

Let $R$ be a commutative Noetherian ring with non-zero identity and $I$ be an ideal of $R$. Let $M$ and $N$ be two finitely generated $R$-modules. In this paper it is shown that, if ${\rm cd}(I,R)\leq 1$ and ${\rm pd_{R}}(M)<\infty$, then $H_{I}^{i}(M,N)$ are $I$-cofinite for each $i\geq 0$. Moreover, it is shown that if $\mbox{q}(I,R) \leq 1$ and ${\rm pd_{R}}(M)<\infty$, then the Bass numbers of generalized local cohomology modules $H_{I}^{i}(M,N)$ are finite for each $i\geq 0$. We also characterize the greatest integer $i$ such that $H_{I}^{i}(M,N)$ is not Artinian and $I$-cofinite.

Citation

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Farzaneh Vahdanipour. Kamal Bahmanpour. Ghader Ghasemi. "On the cofiniteness of generalized local cohomology modules." Bull. Belg. Math. Soc. Simon Stevin 27 (4) 557 - 566, november 2020. https://doi.org/10.36045/j.bbms.190211

Information

Published: november 2020
First available in Project Euclid: 20 November 2020

MathSciNet: MR4177394
Digital Object Identifier: 10.36045/j.bbms.190211

Subjects:
Primary: 13D45, 13E05, 14B15

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 4 • november 2020
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