%0 Journal Article
%A Hempel, Nadja
%A Palacín Cruz, Daniel
%T Division rings with ranks
%D 2018
%@ 0002-9939
%@ 1088-6826
%U https://hdl.handle.net/20.500.14352/98554
%X Any superrosy division ring is shown to be centrally finite. Furthermore, division rings satisfying a generalized chain condition on definable subgroups are studied. In particular, a division ring of burden n has dimension at most n over its center, and any definable group of definable automorphisms of a field of burden n has size at most n. Additionally, an alternative proof that division rings interpretable in o-minimal structures are algebraically closed, real closed or the quaternions over a real closed field is given.
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