Please give me a solution for the following problem: Let $D $ be a division ring and $n$ a positive integer. Then for each left ideal $I$ of $M_n (D) $, there are an invertible matrix $P$ and an integer $r$ with $0\leq r\leq n $ such that $I=PH_r(D)P^{-1} $ where $H_r(D)$ is the set of all matrices with zero in their jth column for all $0 <j\leq n $.
2026-03-25 04:41:33.1774413693
A characterization of left ideals in the ring of n×n matrices over a division ring
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