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Certain simple maximal subfields in division rings. (English) Zbl 07144874

Summary: 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 \(D\).

MSC:

16K20 Finite-dimensional division rings
16R50 Other kinds of identities (generalized polynomial, rational, involution)
17A35 Nonassociative division algebras
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References:

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