On normal subgroups of division rings which are radical over a proper division subring

Triangulaizability of Algebras Over Division Rings

Writing representations over proper sub-division rings

Let E be a division ring and G a finite group of automorphisms of E whose elements are distinct modulo inner automorphisms of E. Given a representation ρ : A → GLd(E) of an F-algebra A, we give necessary and sufficient conditions for ρ to be writable over F = E, i.e. whether or not there exists a matrix A in GLd(E) that conjugates ρ(A) into GLd(F). We give an algorithm for constructing an A, or...

On nest modules of matrices over division rings

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

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...

triangulaizability of algebras over division rings