Bulletin of the
Korean Mathematical Society BKMS

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