## 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

### Keywords:

division ring; rational identity; maximal subfield
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### References:

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