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Separably closed fields with Hasse derivations. (English) Zbl 1039.03031

Summary: In 1995, M. Messmer and C. Wood [ibid. 60, 898–910 (1995; Zbl 0841.03019)] proved quantifier elimination for separably closed fields of finite Ershov invariant \(e\) equipped with a (certain) Hasse derivation. We propose a variant of their theory, using a sequence of \(e\) commuting Hasse derivations. In contrast to Messmer and Wood’s approach, our Hasse derivations are iterative.

MSC:

03C60 Model-theoretic algebra
12L12 Model theory of fields
03C10 Quantifier elimination, model completeness, and related topics

Citations:

Zbl 0841.03019
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References:

[1] Notes on the stability of separably closed fields 44 pp 412– (1979)
[2] Journal of Mathematics of Kyoto University 2 pp 294– (1963)
[3] Separably closed fields with higher derivations. I 60 pp 898– (1995)
[4] DOI: 10.1007/978-3-540-68521-0_9 · doi:10.1007/978-3-540-68521-0_9
[5] Differential galois theory in positive characteristic (2001)
[6] Commutative ring theory (1986)
[7] Journal für die Reine und Angewandte Mathematik 177 pp 215– (1937)
[8] DOI: 10.1007/978-3-662-22174-7_4 · doi:10.1007/978-3-662-22174-7_4
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