Abstract
Let H be a division ring of finite dimension over its center, let H[T] be the ring of polynomials in a central variable over H, andletH(T) be its quotient skew field. We show that every intermediate division ring between H and H(T) is itself of the form H(f)forsome f in the center of H(T). This generalizes the classical Lüroth’s theorem. More generally, we extend Igusa’s theorem characterizing the transcendence degree 1 subfields of rational function fields, from fields to division rings.
Original language | English |
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Pages (from-to) | 261-274 |
Number of pages | 14 |
Journal | Osaka Journal of Mathematics |
Volume | 61 |
Issue number | 2 |
State | Published - Apr 2024 |
All Science Journal Classification (ASJC) codes
- General Mathematics