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Let $(K, v)$ be a Henselian field with a residue field $\widehat K$ and valuegroup $v(K)$, and let $\mathbb{P}$ be the set of prime numbers. This paperfinds conditions on $K$, $v(K)$ and $\widehat K$ under which every algebraicassociative 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 isomorphicto a $K$-subalgebra $\widetilde \Delta $ of $\widetilde R$.

On algebraic central division algebras over Henselian fields of finite absolute Brauer $p$-dimensions and residually arithmetic type