Is semi-simple Lie algebra $L$, satisfy $ L\in{\rm Max}-\triangleleft$?

Question

A Lie algebra $L$ satisfy the maximum condition for ideals, if for each , ascending chain $H_{1} \subseteq H_{2} \subseteq \ldots $ an index $m$ exists such that $H_{i}=H_{k}$ if $m<i$, $m<k .$

We say in short: $ L\in{\rm Max}-\triangleleft$.

Is every semi-simple Lie algebra $L$, satisfy $ L\in{\rm Max}-\triangleleft$?

If its true, how can i prove it?

Answer 1

Hint: Can a semisimple Lie algebra have infinitely many ideals?