Artin-Schreier extensions in NIP and simple fields
نویسندگان
چکیده
منابع مشابه
Artin-schreier Extensions in Dependent and Simple Fields
We show that dependent elds have no Artin-Schreier extension, and that simple elds have only a nite number of them.
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Proof. We prove by the following steps: y 1 Start with induction on n, for n = 1 the result is trivial. y 2 Let g be such that σ1(g) ̸= σ2(g) and consider ∑ aiσi(gx) = 0 and ∑ aiσ1(g)σi(x) = 0 y 3 Cancel one summand by showing a2 = 0 and eventually show all ai = 0 One can prove by induction. Let a1σ1 ≡ 0 then since σ1 does not map to 0 ∈ K one must have a1 = 0. Suppose now that for any linear co...
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We give a method for efficiently computing isomorphisms between towers of Artin-Schreier extensions over a finite field. We find that isomorphisms between towers of degree pn over a fixed field Fq can be computed, composed, and inverted in time essentially linear in pn. The method relies on an approximation process.
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2011
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-011-0104-7