Functional Identities on Upper Triangular Matrix Algebras

Let , be the algebra of upper triangular r×r matrices over field aF. We describe multilinear maps , where n≤r, such that f(A,...,A), A]=0 for all , provided that |F| >n + 1. As an application of the results obtained, we describe linear automorphisms θ of such that θ(A²), θ(A)]=0 for all . Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15, 2000.