ANNIHILATORS OF POWER VALUES OF b-GENERALIZED DERIVATIONS IN PRIME RINGS

Abstract

Let R be a prime ring with extended centroid C and maximal left ring of quotients Qml(R). For a nonzero element b 2 R, let T : R → R be a right b-generalized derivation associated with the map d of R. Suppose that s (T (x))n = O for all x 2 R where s is a nonzero element in R and n ≥ 1 is a fixed positive integer. Then there exist some c 2 Qml(R) and β 2 C such that d(x) = adc(x), T (x) = (c + β)xb for all x 2 R and either s(c + β) = O or b(c + β) = O.