Some matrix groups over finite-dimensional division algebras

Triangularization over finite-dimensional division rings using the reduced trace

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...

Decomposition of Finite - Dimensional Matrix Algebras over F q

Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field Fq(y), where Fq is the finite field with q elements. A fi...

Modules with Few Types over Some Finite-Dimensional Algebras

Triangulaizability of Algebras Over Division Rings

triangularization over finite-dimensional division rings using the reduced trace

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 firs...