Linear groups over a locally linear division ring

TL;DR

This paper introduces new classes of division rings that extend centrally finite division rings, constructs examples of these rings, and studies their linear groups, generalizing previous results in the field.

Contribution

It defines new classes of division rings, constructs non-trivial examples, and extends known results about linear groups over these rings.

Findings

Defined classes of division rings beyond centrally finite

Constructed explicit examples of these rings

Generalized existing results on linear groups over division rings

Abstract

In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined classes. Further, we study linear groups over division rings of these classes. Our new obtained results generalize precedent results for centrally finite division rings.