Triangularizability of algebras over division rings (Q949093)

Let \(V\) be a finite-dimensional right vector space over a 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. A good survey of such results can be found in the book by \textit{H. Radjavi} and \textit{P. Rosenthal} [Simultaneous triangularization. New York, NY: Springer (2000; Zbl 0981.15007)]. The present author aims to generalize some of these results to the case of vector spaces over division rings. Let \(C\) be a left Artinian ring of linear transformations. A block triangularization theorem for \(C\) is proved. Then the theorem is used to extend two well-known results in the theory of triangularization.