The universality of Hughes-free division rings

Triangulaizability of Algebras Over Division Rings

Explicit Free Groups in Division Rings

Let D be a division ring of characteristic 6= 2 and suppose that the multiplicative group D• = D \ {0} has a subgroup G isomorphic to the Heisenberg group. Then we use the generators of G to construct an explicit noncyclic free subgroup of D•. The main difficulty occurs here when D has characteristic 0 and the commutators in G are algebraic over Q.

The Universality of Asymmetric Division

Copyright: © 2011 Canelles M. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Asymmetric division, a process by which stem cells divide to generate the diversity of cell types that populate adult organisms, ha...

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...

Free Symmetric and Unitary Pairs in Division Rings with Involution

Let D be a division ring with an involution and characteristic different from 2. Then, up to a few exceptions, D contains a free pair of symmetric elements provided that (a) it is finite-dimensional and the center has a finite sufficiently large transcendence degree over the prime field, or (b) the center is uncountable, but not algebraically closed in D. Under conditions (a), if the involution...