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arXiv · 1808.08452

A note On subgroups in a division ring that are left algebraic over a division subring

Bui Xuan Hai·Vu Mai Trang·Mai Hoang Bien
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Abstract

Let $D$ be a division ring with center $F$ and $K$ a division subring of $D$. In this paper, we show that a non-central normal subgroup $N$ of the multiplicative group $D^*$ is left algebraic over $K$ if and only if so is $D$ provided $F$ is uncountable and contained in $K$. Also, if $K$ is a field and the $n$-th derived subgroup $D^{(n)}$ of $D^{*}$ is left algebraic of bounded degree $d$ over $K$, then $\dim_FD\le d^2$.

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Bui Xuan Hai, Vu Mai Trang, Mai Hoang Bien. 2018-08-25. A note On subgroups in a division ring that are left algebraic over a division subring. https://doi.org/10.1007/s00013-019-01317-6

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