Power linear Keller maps with ditto triangularizations

We show that power linear Keller maps F=(x1+d(A1x),x2+d(A2x),…,xn+d(Anx)) are linearly triangularizable if (1) rkA⩽2 or (2) corkA⩽2 and d⩾3 or (3) corkA=3, d⩾5 and the diagonal of A is nonzero. Furthermore, we show that the triangularizations can be chosen power linear as well.