Why is the upper triangular matrices over a division ring D is artinian? I tried to find properties of this class of rings. The only thing I found that the jacobson radical of this ring is the strictly upper triangular matrices over D. Thankyou.
2026-05-06 02:45:11.1778035511
$UTM_n[D]$ is artinian
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Hint: right ideals are also right $D$-subspaces. What can you say about the $D$-dimension of $UTM_n(D)$?
The same argument works on the left side.