Triangularization over finite-dimensional division rings using the reduced trace

Document Type: Research Paper

Author

Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman

Abstract

In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one is a generalization of a result due to Kaplansky and in the second one a triangularizability condition which is dependent on a single element is presented.

Keywords


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