Splitting field of a central simple algebra
= Splitting field of a central simple algebra
{title2=$A_E\cong M_d(E)$}
An extension $E/K$ splits a <central simple algebra> $A$ of degree $d$ when $A\otimes_KE\cong M_d(E)$. A finite separable splitting field exists. Splitting is preserved by further scalar extension and is equivalent to the vanishing of the restricted <Brauer group> class.