On a multilinear generalized polynomial identity in division algebras

Let [Formula: see text] be a division algebra over its center [Formula: see text] of characteristic [Formula: see text]. Let [Formula: see text] have a minimal polynomial over [Formula: see text] of degree at least [Formula: see text] and [Formula: see text] for all [Formula: see text]. Let [Formula: see text] be the standard polynomial of degree [Formula: see text]. Then [Formula: see text] for all [Formula: see text] implies that [Formula: see text] for all [Formula: see text].