On the residue fields of Henselian valued stable fields, II

Details On the residue fields of Henselian valued stable fields, II On the residue fields of Henselian valued stable fields, II

2007-04-12

arxiv.org/abs/0704.1557v1

Mathematics

Rings and Algebras

10 pages

Scientific paper

Let $E$ be a primarily quasilocal field, $M/E$ a finite Galois extension and $D$ a central division $E$-algebra of index divisible by $[M\colon E]$. In addition to the main result of Part I, this part of the paper shows that if the Galois group $G(M/E)$ is not nilpotent, then $M$ does not necessarily embed in $D$ as an $E$-subalgebra. When $E$ is quasilocal, we find the structure of the character group of its absolute Galois group; this enables us to prove that if $E$ is strictly quasilocal and almost perfect, then the divisible part of the multiplicative group $E ^{\ast}$ equals the intersection of the norm groups of finite Galois extensions of $E$.

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