A theorem of Kaplansky revisited

作者：Radjavi Heydar; Yahaghi Bamdad R^*

来源：Linear Algebra and Its Applications, 2015, 487: 268-275.

DOI：10.1016/j.laa.2015.09.024

• Semigroup
• Division ring
• Spectra
• Irreducibility
• Triangularizability

We present a simple proof of a theorem due to Kaplansky which unifies theorems of Kolchin and Levitzki on triangularizability of semigroups of matrices. We also give two different extensions of the theorem. As a consequence, we prove the counterpart of Kolchin's Theorem for finite groups of unipotent matrices over division rings.

• 出版日期2015-12-15