ON FUNCTIONAL IDENTITIES AND COMMUTING ADDITIVE MAPPINGS

We study functional identities of degree m. As an application of obtai ned results, we describe additive mappings f(i): A --> A of a prime ri ng A satisfying a functional identity of the form Sigma(i-0)(n)x(2)f(i )(x)x(n-i) =0 provided that A is not algebraic of bounded degree less than or equal to n over the extended centroid. A number of results on k-commuting additive mappings and commuting traces of m-additive mappi ngs, obtained earlier, are special cases of our ones.