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 M_(n)(D)has a strictly maximal subf...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 M_(n)(D)has a strictly maximal subfield which is Galois(resp.,abelian)over E if and only if M_(n)(D)has a strictly maximal subfield K which is Galois(resp.,abelian)and tame over E withГ_(K)■Г_(D),whereГ_(K)andГ_(D)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.展开更多
文摘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 M_(n)(D)has a strictly maximal subfield which is Galois(resp.,abelian)over E if and only if M_(n)(D)has a strictly maximal subfield K which is Galois(resp.,abelian)and tame over E withГ_(K)■Г_(D),whereГ_(K)andГ_(D)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.
