On artinianness of general local cohomology modules
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 689-698
https://doi.org/10.4134/BKMS.b200469
Published online May 10, 2021
Printed May 31, 2021
Nguyen Minh Tri
4 Le Quy Don Street, Tan Hiep Ward, Bien Hoa City
Abstract : In this paper, we show some results on the artinianness of local cohomology modules with respect to a system of ideals. If $M$ is a $\Phi$-minimax ZD-module, then $H^{\dim M}_\Phi(M)/\a H^{\dim M}_\Phi(M)$ is artinian for all $\a\in \Phi.$ Moreover, if $M$ is a $\Phi$-minimax ZD-module, $t$ is a non-negative integer and $H^i_\Phi(M)$ is minimax for all $i>t,$ then $H^i_\Phi(M)$ is artinian for all $i>t.$
Keywords : Artinianness, local cohomology, system of ideals, $\Phi$-minimax, ZD-modules
MSC numbers : Primary 13D45, 13E10
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