2023/04/21 by François Legrand, Legrand, François, Elad Paran +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2304.10738
openalex publication_date 2023/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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, and let H(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), for some 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.