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Certain simple maximal subfields in division rings

Mehdi Aaghabali; Mai Hoang Bien — 2019

Czechoslovak Mathematical Journal

Let $D$ be a division ring finite dimensional over its center $F$ . The goal of this paper is to prove that for any positive integer $n$ there exists $a \in D^{(n)},$ the $n$ th multiplicative derived subgroup such that $F (a)$ is a maximal subfield of $D$ . We also show that a single depth- $n$ iterated additive commutator would generate a maximal subfield of $D .$

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