On artinianness of general local cohomology modules
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 689-698
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
Downloads: Full-text PDF   Full-text HTML


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd