A theorem of Kaplansky revisited

被引：2

作者：

Radjavi, Heydar ^{[1
]}

Yahaghi, Bamdad R. ^{[2
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

[2] Golestan Univ, Dept Math, Fac Sci, Gorgan 193955746, Iran

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 487卷

关键词：

Semigroup; Division ring; Spectra; Irreducibility; Triangularizability; SEMIGROUPS; MATRICES;

D O I：

10.1016/j.laa.2015.09.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：268 / 275

页数：8

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