Model theory of fields with free operators in positive characteristic
Transactions of the American Mathematical Society, cilt.372, sa.8, ss.5991-6016, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 372 Sayı: 8
- Basım Tarihi: 2019
- Doi Numarası: 10.1090/tran/7896
- Dergi Adı: Transactions of the American Mathematical Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.5991-6016
- Anahtar Kelimeler: Derivations in positive characteristic, Model companion, Operator
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We give algebraic conditions for a finite commutative algebra B over a field of positive characteristic, which are equivalent to the companionability of the theory of fields with “B-operators” (i.e., the operators coming from homomorphisms into tensor products with B). We show that, in the most interesting case of a local B, these model companions admit quantifier elimination in the “smallest possible” language, and they are strictly stable. We also describe the forking relation there.