Images of multilinear polynomials on n × n upper triangular matrices over infinite fields

In this paper we prove that the image of multilinear polynomials evaluated on algebra UTn(K) n × upper triangular matrices over an infinite field K equals Jr, a power its Jacobson ideal J = J(UTn(K)). particular, shows analogue Lvov—Kaplansky conjecture for is true, solving Fagundes and de Mello. To fact, introduce notion commutator-degree polynomial characterize r in terms coefficients. It turns out f Jr if only has r.