On algebraic closure in pseudofinite fieldso
Journal of Symbolic Logic, cilt.77, sa.4, ss.1057-1066, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 77 Sayı: 4
- Basım Tarihi: 2012
- Doi Numarası: 10.2178/jsl.7704010
- Dergi Adı: Journal of Symbolic Logic
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1057-1066
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We study the automorphism group of the algebraic closure of a substructure A of a pseudo- finite field F . We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F . For almost all completions of the theory of pseudofinite fields, we show that over A, algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field. © 2012, Association for Symbolic Logic.