  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 $\Delta $ of $R$ is isomorphic
to a $K$-subalgebra $\widetilde \Delta $ of $\widetilde R$.
