@article { author = {Momenaee Kermani, Hossein}, title = {Triangularization over finite-dimensional division rings using the reduced trace}, journal = {Wavelet and Linear Algebra}, volume = {3}, number = {2}, pages = {69-74}, year = {2016}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2016.23241}, 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 = {Triangularizable,Semigroup,Irreducible,Division ring,Reduced trace}, url = {https://wala.vru.ac.ir/article_23241.html}, eprint = {https://wala.vru.ac.ir/article_23241_1e8aafe10279931fe51e54733c2efcbc.pdf} }