zbMATH — the first resource for mathematics

Separably closed fields with higher derivations. I. (English) Zbl 0841.03019
Summary: We define a complete theory \(SHF_e\) of separably closed fields of finite invariant \(e\) (= degree of imperfection) which carry an infinite stack of Hasse-derivations. We show that \(SHF_e\) has quantifier elimination and eliminates imaginaries.

03C60 Model-theoretic algebra
12L12 Model theory of fields
03C10 Quantifier elimination, model completeness and related topics
Full Text: DOI
[1] Algebra i Logika 3 pp 368– (1990)
[2] Journal für Mathematik 175 pp 50– (1936)
[3] Supplément au Bulletin de la Société Mathématique de France 116 (1988)
[4] Model theory (1973)
[5] Notes on the stability of separably closed fields 44 pp 412– (1979)
[6] DOI: 10.1007/BF02757008 · Zbl 0346.02030 · doi:10.1007/BF02757008
[7] Prime model extensions for differential fields of characteristic p 0 39 pp 469– (1974)
[8] Proceedings of the American Mathematical Society 40 pp 577– (1973)
[9] Cours de théorie des modèles (1987)
[10] Une théorie de Galois imaginaire 48 pp 1151– (1983)
[11] Transactions of the American Mathematical Society
[12] Journal of Mathematics of Kyoto University 2 pp 294– (1963)
[13] Differential algebra and algebraic groups (1973)
[14] Lectures in abstract algebra III (1964)
[15] Doklady Akadéemii Nauk SSSR 174 pp 19– (1967)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.