Rational Places on Algebraic Function Fields over Generalized Closed Fields Original Research Article

The theorem of Lang asserting that a formally real finitely generated field extension of a real closed field admits a rational place is generalized here. In this generalization, the "formally real extensions" and "real closed fields" of Lang′s theorem are replaced by the "admissible extensions" and "closed fields" of R. Brown (J. Algebra169 (1994), 751-774). Knebusch′s theorem combining Lang′s rational place existence theorem and Lang′s imbedding theorem is also generalized. The existence of rational places with various special properties is proved; one such result includes Prestel and Roquette′s rational place existence theorem for formally p-adic algebraic function fields over p-adically closed fields.