The theory of modules of separably closed fields. I. (English) Zbl 1013.03042

Summary: We consider separably closed fields of characteristic \(p>0\) and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the \(p\)-component functions.


03C60 Model-theoretic algebra
12L12 Model theory of fields
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[1] Supplément au Bulletin de la Société Mathématique de France pp 116– (1988)
[2] Encyclopedia of mathematics and its applications 57 (1995)
[3] Sous-groupes infiniment définissables du groupe additif d’un corps séparablement clos (2001)
[4] DOI: 10.1016/0168-0072(84)90014-9 · Zbl 0593.16019 · doi:10.1016/0168-0072(84)90014-9
[5] Notes on the stability of separably closed fields 44 pp 412– (1979)
[6] Doklady 174 pp 19– (1967)
[7] London Mathematical Society Lecture Notes Series 130 (1988)
[8] DOI: 10.1090/S0002-9947-1933-1501703-0 · doi:10.1090/S0002-9947-1933-1501703-0
[9] Definability in reducts of algebraically closed fields 53 pp 188– (1988)
[10] Basic algebra I (1985)
[11] DOI: 10.2307/1968173 · Zbl 0007.15101 · doi:10.2307/1968173
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