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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.

MSC:

03C60 Model-theoretic algebra
12L12 Model theory of fields
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[2] Encyclopedia of mathematics and its applications 57 (1995)
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[4] DOI: 10.1016/0168-0072(84)90014-9 · Zbl 0593.16019 · doi:10.1016/0168-0072(84)90014-9
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[11] DOI: 10.2307/1968173 · Zbl 0007.15101 · doi:10.2307/1968173
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