COMMUTING MAPPINGS ON RIGHT IDEALS IN PRIME RINGS

Abstract

Let R be a prime ring of characteristic different from 2, with extended centroid C, d and g derivations of R, I a non-zero right ideal of R and s4 the standard identity of degree 4. If [d([x,y]),[x,y]][x,y]− [x,y][g([x,y]),[x,y]] = 0, for all x,y ∈ I, then one of the following holds: (i) s4(x1,x2,x3,x4)x5 is an identity for I; (ii) d(x)=[a,x], with (a−α)I = 0 for a suitable α ∈ C and g =0 .