Large subfields and small subfields

Mikihiko Endo
1972 Proceedings of the Japan Academy  
We study subfields of large fields which are generated by infinite existentially definable subsets. We say that such subfields are existentially generated. Let L be a large field of characteristic exponent p, and let E ⊆ L be an infinite existentially generated subfield. We show that E contains L (p n ) , the p n -th powers in L, for some n < ω. This generalises a result of Fehm from [4] , which shows E = L, under the assumption that L is perfect. Our method is to first study existentially
more » ... existentially generated subfields of henselian fields. Since L is existentially closed in the henselian field L((t)), our result follows.
doi:10.3792/pja/1195519538 fatcat:yhrinh6uivcmdhhro3gbasjaxm