Linear groups over a locally linear division ring
Bui Xuan Hai, Mai Hoang Bien, Trinh Thanh Deo

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.
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Taxonomy
TopicsRings, Modules, and Algebras · Finite Group Theory Research · Advanced Topics in Algebra
