An Engel condition with an additive mapping in semiprime ringsFošner, Maja (Avtor) Rehman, Nadeem Ur (Avtor) Vukman, Joso (Avtor) , Indian Academy of Sciences (Lastnik avtorskih pravic) mathematicsalgebrasemiprime ringsderivationThe main purpose of this paper is to prove the following result: Let n > 1 be a fixed integer, let R be a n!-torsion free semiprime ring, and let f : R -> R be an additive mapping satisfying the relation [f (x), x]n = [[. . . [[f (x), x], x], . . .], x] = 0 for all x = R. In this case [f (x), x] = 0 is fulfilled for all x = R. Since any semisimple Banach algebra (for example, C algebra) is semiprime, this purely algebraic result might be of some interest from functional analysis point of view.20142017-06-27 13:31:43Znanstveno delo66472sl