Kummer subfields of tame division algebras over Henselian valued fields

Details Kummer subfields of tame division algebras over Henselian valued fields Kummer subfields of tame division algebras over Henselian valued fields

2007-06-15

arxiv.org/abs/0706.2350v1

Mathematics

Rings and Algebras

17 pages

Scientific paper

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^n over E such that p\neq char(\bar E) and rk(\Gamma_D/\Gamma_E)\geq 3 [resp., such that p\neq char(\bar E) and p^3 divides exp(\Gamma_D/\Gamma_E)], then D is non-cyclic [Proposition 3.1] [resp., D is not an elementary abelian crossed product [Proposition 3.2]].

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