Defining transcendentals in function fields
Copyright policy )Defining transcendentals in function fields
AbstractGiven any fieldK, there is a function fieldF/Kin one variable containing definable transcendental overK, i.e., elements inF / Kfirst-order definable in the language of fields with parameters fromK. Hence, the model-theoretic and the field-theoretic relative algebraic closure ofKinF do notcoincide. E.g., ifKis finite, the model-theoretic algebraic closure ofKin the rational function fieldK(t)isK(t).For the proof, diophantine ∅-definability ofKinFis established for any function fieldF/Kin one variable, providedKis large, orK×/(K×)nis finite for some integern> 1 coprime tochar K.
- University of Oxford United Kingdom
- University of Konstanz Germany
- University of Freiburg Germany
automorphism, 12F99, groups of function fields, Model-theoretic algebra, algebraic closure, 03C60, 12L12, Model theory of fields
automorphism, 12F99, groups of function fields, Model-theoretic algebra, algebraic closure, 03C60, 12L12, Model theory of fields
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