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arXiv · 1605.04118

Division Rings with Ranks

Nadja Hempel·Daniel Palacín
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Abstract

Any superrosy division ring (i.e. a division ring equipped with an abstract notion of rank) 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, interpretable division rings in o-minimal structures are shown to be algebraically closed, real closed or the quaternions over a real closed field.

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Nadja Hempel, Daniel Palacín. 2016-05-13. Division Rings with Ranks. https://arxiv.org/abs/1605.04118

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