On a functional equation related to two-sided centralizers - Kosi-Ulbl, Irena (Annales Mathematicae Silesianae, 2018)
The main aim of this manuscript is to prove the following result. Let n>2 be a fixed integer and R be a k-torsion free semiprime ring with identity, where k∈2, n−1, n. Let us assume that for the additive mapping T:R→R 3T(xn) = T(x)xn-1 + xT(xn-2)x + xn-1T(x), x∈R, is also fulfilled. Then T is a two-sided centralizer.