PRIME RINGS WITH ANNIHILATOR CONDITIONS ON POWER VALUES OF DERIVATIONS ON MULTILINEAR POLYNOMIALS

Abstract

Let R be a prime algebra over a commutative ring K, d anonzero derivation of R, f(x1, .., xn) a multilinear polynomial over K inn non-commuting variables, a 2 R and m 1 a fixed integer. Supposethat f(x1, .., xn) is not central on R. If a(d(f(r1, .., rn)))m = 0, for anyr1, .., rn 2 R, then a = 0.