Certain Simple Maximal Subfields in Division Rings

TL;DR

This paper proves the existence of elements in division rings whose generated fields are maximal subfields, using multiplicative derived subgroups and additive commutators, advancing understanding of the structure of division rings.

Contribution

It establishes the existence of elements in division rings that generate maximal subfields via multiplicative derived subgroups and additive commutators, providing new structural insights.

Findings

Existence of elements in D^(n) generating maximal subfields

Single depth-n additive commutator can generate a maximal subfield

Results apply to division rings finite over their centers

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.