m-commuting Additive Maps on Upper Triangular Matrices Rings

Abstract

Let T_n(R) be the upper triangular matrix ring over a unital commutative ring whose characteristic is not a divisor of m. Suppose that f : T_n(R) → T_n(R) is an additive map such that X^mf (X) = f (X)X^m for all X ϵ T_n(R), where m ≥ 1 is an integer. We consider the problem of describing the form of the map X → f (X).