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INICIO |
27 de julio de 2024
On Ø-definable elements in a field
| Título inglés | On Ø-definable elements in a field |
|---|---|
| Título español | Elementos Ø-definibles en un campo. |
| Autor/es | Tyszka, Apoloniusz |
| Organización | Tech. Fac. Hugo Kollataj Univ., Cracovia, Polonia |
| Revista | 0010-0757 |
| Publicación | 2007, 58 (1): 73-84, 17 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | We develop an arithmetic characterization of elements in a field which are first-order definable by a parameter-free existential formula in the language of rings. As applications we show that in fields containing any algebraically closed field only the elements of the prime field are existentially Æ-definable. On the other hand, many finitely generated extensins of Q contain existentially Æ-definable elements which are transcendental over Q. Finally, we show that all transcendental elements in R having a recursive approximation by rationals, are definable in R(t), and the same holds when one replaces R by any Pythagorean subfield of R. |
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