Geodesic
Certain simple maximal subfields in division rings
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1053-1060
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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 $D.$
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 $D.$
DOI : 10.21136/CMJ.2019.0039-18
Classification : 16K20, 16R50, 17A35
Keywords: division ring; rational identity; maximal subfield 
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Aaghabali, Mehdi; Bien, Mai Hoang. Certain simple maximal subfields in division rings. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1053-1060. doi: 10.21136/CMJ.2019.0039-18

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