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arXiv · 1308.6602

Free structures in division rings

Renato Fehlberg Júnior
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Abstract

Makar-Limanov's conjecture states that if a division ring D is finitely generated and infinite dimensional over its center k then D contains a free k-subalgebra of rank 2. In this work, we will investigate the existence of such structures in D, the division ring of fractions of the skew polynomial ring L[t;σ], where t is a variable and $σ$ is a k-automorphism of L. For instance, we prove Makar-Limanov's conjecture when either L is the function field of an abelian variety or the function field of the n-dimensional projective space.

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Renato Fehlberg Júnior. 2013-08-29. Free structures in division rings. https://arxiv.org/abs/1308.6602

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