Abstract We will show that every nilpotent element N in , the ring of square matrices over a division ring, can be presented as a single commutator, that is, for some matrices A, B in . We will also construct an example illustrating that there exists a prime ring with unity over which some nilpotent matrices cannot be presented as commutators.

中文翻译：

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将幂零矩阵表示为单个换向器

摘要 我们将证明每个幂零元 N in ，除环上的方阵环，可以表示为单个交换子，即对于某些矩阵 A, B in 。我们还将构建一个示例，说明存在一个具有统一性的素环，在该环上某些幂零矩阵不能表示为交换子。