Journal of the
Korean Mathematical Society JKMS

Let $L/F$ be a finite separable extension of Henselian valued fields with same residue fields $\bar L =\bar F$. Let $D$ be an inertially split division algebra over $L$, and let $^cD$ be the underlying division algebra of the corestriction $\text{cor}_{L/F} (D)$ of $D$. We show that the index $\text{ind}(^cD)$ of $^cD$ divides $[Z(\bar D)\ :\ Z(\overline{^cD})]\cdot \ \text{ind}(D)$, where $Z(\bar D)$ is the center of the residue division ring $\bar D$.

Keywords: Corestriction, Division Algebras, Henselian valuation

MSC numbers: 16K20