Let $F_0$ be an absolutely algebraic field of characteristic $p>0$ and
$\kappa$ an infinite cardinal. It is shown that there exists a
field $F$ such that $F^*\cong F^*_0\oplus(\oplus_\kappa
\mathbb{Q})$ with $Br(F)=\{0\}$. Let $L$ be an algebraic closure
of $F$. Then for any finite subextension $K$ of $L/F$, we have
$K^*\cong T(K^*)\oplus(\oplus_\kappa \mathbb{Q})$, where $T(K^*)$
is the group of torsion elements of $K^*$. In addition,
$Br(K)=\{0\}$ and $[K:F]=[T(K^*) \cup \{0\}:F_0]$.
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 16 Temmuz 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 32 Sayı: 32 |