Finite power-associative 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 first one...

Power-associative Rings of Characteristic Two

Finite Groups Embeddable in Division Rings

In [He], Herstein conjectured that odd-order subgroups of division rings K were cyclic, and he proved this to be the case when K is the division ring of the real quaternions. Herstein’s conjecture was settled negatively in [Am]. As part of his complete classification of finite groups in division rings, Amitsur showed that the smallest noncyclic odd-order group that can be embedded in a division...

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...

Triangulaizability of Algebras Over Division Rings