论文标题
在代数中央分区代数上，有限的绝对brauer $ p $ dimensions和残留算术类型
On algebraic central division algebras over Henselian fields of finite absolute Brauer $p$-dimensions and residually arithmetic type
论文作者
论文摘要
令$（k，v）$为HENSELIAN字段，其中有残留字段$ \ widehat k $和value group $ v（k）$，让$ \ mathbb {p} $是质数的集合。本文在$ k $，$ v（k）$和$ \ widehat k $上找到条件，根据该条件，每个代数协会中央$ k $ k $ -ak $ -algebra $ r $都包含一个中央$ k $ -k $ -subalgebra $ \ widetilde r $ r $ r $ r $ r $ decomposable r $ decomposable可在中央$ k $ k $ -subalgebras $ -subalgebras $ ras $ ras $ ry $ rs $ r r y _ _ _ _ _ p.p}中有限$ p $ - 主要尺寸$ [r _ {p} \ colon k] $的\ mathbb {p} $，使每个有限尺寸$ k $ -subalgebra $ r $ r $ is $ r $ is osomorphic in A $ k $ k $ k $ -subalgebra $ \ wideteTeLde $ $ $ $
Let $(K, v)$ be a Henselian field with a residue field $\widehat K$ and value group $v(K)$, and let $\mathbb{P}$ be the set of prime numbers. This paper finds conditions on $K$, $v(K)$ and $\widehat K$ under which every algebraic associative central division $K$-algebra $R$ contains a central $K$-subalgebra $\widetilde R$ decomposable into a tensor product of central $K$-subalgebras $R _{p}$, $p \in \mathbb{P}$, of finite $p$-primary dimensions $[R _{p}\colon K]$, such that each finite-dimensional $K$-subalgebra $Δ$ of $R$ is isomorphic to a $K$-subalgebra $\widetilde Δ$ of $\widetilde R$.
