Kummer subfields of tame division algebras over Henselian valued fields
نویسنده
چکیده
By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [resp., such that p 6= char(Ē) and p 3 divides exp(ΓD/ΓE)], then D is non-cyclic [Proposition 3.1] [resp., D is not an elementary abelian crossed product [Proposition 3.2]].
منابع مشابه
Subfields of Nondegenerate Tame Semiramified Division Algebras
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