Let $(K,v)$ be a Henselian discrete valued field with a quasifinite residue field. This paper proves the existence of an algebraic extension $E/K$ satisfying the following: (i) E has dimension dim$(E)\le 1$, i.e. the Brauer group Br$(E^{\prime })$ is trivial, for every algebraic extension $E^{\prime }/E$; (ii) finite extensions of E are not $C_1$-fields. This, applied to the maximal algebraic extension K of the field $\mathbb{Q}$ of rational numbers in the field ${\mathbb{Q}}_p$ of p-adic numbers, for a given prime p, proves the existence of an algebraic extension $E_p/\mathbb{Q}$, such that dim$(E_p)\le 1$, $E_p$ is not a $C_1$-field, and $E_p$ has a Henselian valuation of residual characteristic p.

让$(ķ,v)$是具有准有限余数场的 Henselian 离散值场。本文证明了代数推广的存在$乙/ķ$满足以下条件： (i) E具有维度 dim$(乙)\le 1$, 即布劳尔群 Br$({乙}^{\text{'}})$是微不足道的，对于每个代数扩展${乙}^{\text{'}}/乙$; (ii) E的有限扩展不是$C_1$-字段。这适用于场的最大代数扩展K$\mathbb{问}$领域中的有理数${\mathbb{问}}_p$的p进数，对于给定的素数p，证明代数扩展的存在${乙}_p/\mathbb{问}$, 这样暗$({乙}_p)\le 1$,${乙}_p$不是一个$C_1$-字段，和${乙}_p$对残差特征p有 Henselian 估值。