On right α-centralizers and commutativity of prime rings

الملخص EN

Let R be a prime ring, U be a lie ideal of R, and α be an endomorphism of R.

An additive mapping f : R -> R is called a right a-centralizer if f(xy) = a(x)f(y) holds for all x, yεR.

In the present paper, we shall investigate the commutatively of prime rings admitting right a centralizer satisfying any one of the following conditions: (i) f([x,y]) = ±[x,y], (ii) f(xoy) = ±xoy, (iii) f(x2) = ±x2 for all x,yεU.