Momenaee Kermani, H. (2016). Triangularization over finite-dimensional division rings using the reduced trace. Wavelet and Linear Algebra, 3(2), 69-74. doi: 10.22072/wala.2016.23241

Hossein Momenaee Kermani. "Triangularization over finite-dimensional division rings using the reduced trace". Wavelet and Linear Algebra, 3, 2, 2016, 69-74. doi: 10.22072/wala.2016.23241

Momenaee Kermani, H. (2016). 'Triangularization over finite-dimensional division rings using the reduced trace', Wavelet and Linear Algebra, 3(2), pp. 69-74. doi: 10.22072/wala.2016.23241

Momenaee Kermani, H. Triangularization over finite-dimensional division rings using the reduced trace. Wavelet and Linear Algebra, 2016; 3(2): 69-74. doi: 10.22072/wala.2016.23241

Triangularization over finite-dimensional division rings using the reduced trace

^{}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.

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