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Cofiniteness of Generalized Local Cohomology Modules for One-Dimensional Ideals

Published online by Cambridge University Press:  20 November 2018

Kamran Divaani-Aazar  and
Alireza Hajikarimi
Kamran Divaani-Aazar
Affiliation:
Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran e-mail: [email protected]
Alireza Hajikarimi
Affiliation:
Science and Research Branch, Islamic Azad University, Tehran, Iran e-mail: [email protected]
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Abstract

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Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring $R$ and $M$ and $N$ two finitely generated $R$-modules. Our main result asserts that if $R/\mathfrak{a}\,\le \,1$, then all generalized local cohomology modules $H_{\mathfrak{a}}^{i}(M,\,N)$ are $\mathfrak{a}$-cofinite.

Keywords

13D4513E0513E10cofinite modulesgeneralized local cohomology moduleslocal cohomology modules
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 1 , 01 March 2012 , pp. 81 - 87
Copyright
Copyright © Canadian Mathematical Society 2012

References

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