SOME COMMUTATIVITY THEOREMS FOR *-PRIME RINGS WITH (σ, τ)-DERIVATION

Let R be a *-prime ring with center Z(R), d a non-zero (sigma, tau) derivation of R with associated automorphisms sigma and tau of R, such that sigma, tau and d commute with '*'. Suppose that U is an ideal of R such that U* = U, and C-sigma,C-tau = {c epsilon R \ c sigma(x) = tau (x)c for all x epsilon R}. In the present paper, it is shown that if characteristic of R is different from two and [d(U), d(U)](sigma,tau) = {0}, then R is commutative. Commutativity of R has also been established in case if [d(R), d(R)](sigma,tau) subset of C-sigma,C-tau.