Czechoslovak Mathematical Journal, first online, pp. 1-8


Certain simple maximal subfields in division rings

Mehdi Aaghabali, Mai Hoang Bien

Received January 22, 2018.   Published online June 5, 2019.

Abstract:  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 $D.$
Keywords:  division ring; rational identity; maximal subfield
Classification MSC:  16K20, 16R50, 17A35
DOI:  10.21136/CMJ.2019.0039-18

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Affiliations:   Mehdi Aaghabali (corresponding author), School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland; School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran, e-mail: maghabali@gmail.com; Mai Hoang Bien, Faculty of Mathematics and Computer Science, University of Science, VNU-HCM, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam, e-mail: mhbien@hcmus.edu.vn


 
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