On Crossed Product Algebras over Henselian Valued Fields

• 作者: Driss Bennis Karim Mounirh
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 389-404
• 页数: 16页
• 语种: 英文
• DOI: 10.1142/S1005386720000322

摘要

Let D be a tame central division algebra over a Henselian valued field E,D be the residue division algebra of D,E be the residue field of E,and n be a positive integer.We prove that Mn(D) has a strictly maximal subfield which is Galois (resp.,abelian) over (E) if and only if Mn(D) has a strictly maximal subfield K which is Galois (resp.,abelian)and tame over E with ΓK (C) ΓD,where ΓK and ΓD are the value groups of K and D,respectively.This partially generalizes the result proved by Hanke et al.in 2016 for the case n =1.