Radicability condition on GLn(D)

Abstract

Given an indivisible field [Formula: see text], let [Formula: see text] be a finite dimensional noncommutative [Formula: see text]-central division algebra. It is shown that if [Formula: see text] is radicable, then [Formula: see text] is the ordinary quaternion division algebra and [Formula: see text] is divisible. Also, it is shown that when [Formula: see text] is a field of characteristic zero and [Formula: see text], then [Formula: see text] is radicable if and only if for any field extension [Formula: see text] with [Formula: see text], [Formula: see text] is divisible.