Burnside's theorem for matrix rings over division rings*1

Triangulaizability of Algebras Over Division Rings

An Extension of the Theorem on Alternative Division Rings1

On Ordered Division Rings1

1. Ordered groups. Suppose T is a simply ordered set and for each 7 in T let Ry be an additive group. Consider the set H = H(T, Ry) of all vectors ( • • • , ry, ■ • • ) for which ry is in Ry and almost every r"< is zero (i.e., the set of 7's for which ry^0 is inversely well ordered). H is a group w.r.t. (with respect to) vector addition, called the T-sum of the Ry. It the Ry are ordered groups ...

Diagonal Matrix Reduction over Refinement Rings

  Abstract: A ring R is called a refinement ring if the monoid of finitely generated projective R- modules is refinement.  Let R be a commutative refinement ring and M, N, be two finitely generated projective R-nodules, then M~N  if and only if Mm ~Nm for all maximal ideal m of  R. A rectangular matrix A over R admits diagonal reduction if there exit invertible matrices p and Q such that PAQ is...

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...