An Existential Divisibility Lemma for Global Fields

• Autores: Jeroen Demeyer, Jan Van Geel
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 147, Nº 4, 2006, págs. 293-308
• Idioma: inglés
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• Resumen

  • We generalize the Existential Divisibility Lemma by Th. Pheidas [7] to all global fields K of characteristic not 2, and for all sets of primes that are inert in a quadratic extension L of K. We also remove the conditions in real and ramifying primes, which were present in Pheidas¿ version. As a Corollary, we recover the known fact that the set of integral elements at a prime in a global field is existentially definable.