TRIANGULARIZABILITY OF ALGEBRAS OVER DIVISION RINGS

Let V be a finite-dimensional right vector space overa division ring D and let C be a collection of linear transformations on V. In case of vector spaces over fields some authors have derived conditions on C which imply its triangularizability. Here,we will generalize some of these results to the case of vector spaces over division rings. We let C be a left artinian ring of linear transformations and prove a block triangularization theorem for C. Thetheorem is then used to extend two well-known results in the theory of triangularization.