TY - JOUR ID - 23241 TI - Triangularization over finite-dimensional division rings using the reduced trace JO - Wavelet and Linear Algebra JA - WALA LA - en SN - 2383-1936 AU - Momenaee Kermani, Hossein AD - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman Y1 - 2016 PY - 2016 VL - 3 IS - 2 SP - 69 EP - 74 KW - Triangularizable KW - Semigroup KW - Irreducible KW - Division ring KW - Reduced trace DO - 10.22072/wala.2016.23241 N2 - 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. UR - https://wala.vru.ac.ir/article_23241.html L1 - https://wala.vru.ac.ir/article_23241_1e8aafe10279931fe51e54733c2efcbc.pdf ER -