LÜROTH’S AND IGUSA’S THEOREMS OVER DIVISION RINGS

François Legrand, Elad Paran

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)261-274
Number of pages14
JournalOsaka Journal of Mathematics
Volume61
Issue number2
StatePublished - Apr 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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