Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3229
Abstract
Let $(K, v)$ be a Henselian discrete valued field with residue field $\widehat K$ of characteristic $q \ge 0$, and Brd$_{p}(K)$ be the Brauer $p$-dimension of $K$, for each prime $p$. The present paper shows that if $p = q$, then Brd$_{p}(K) \le 1$ if and only if $\widehat K$ is a $p$-quasilocal field and the degree $[\widehat K\colon \widehat K ^{p}]$ is $\le p$. This complements our earlier result that, in case $p \neq q$, we have Brd$_{p}(K) \le 1$ if and only if $\widehat K$ is $p$-quasilocal and Brd$_{p}(\widehat K) \le 1$.
Keywords
Henselian field, stable field, Brauer $p$-dimension, $p$-quasilocal field, almost perfect field
First Page
1735
Last Page
1748
Recommended Citation
CHIPCHAKOV, IVAN
(2022)
"Henselian discrete valued stable fields,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 8.
https://doi.org/10.55730/1300-0098.3229
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/8
