ON (σ, τ )--DERIVATION AND COMMUTATIVITY OF -PRIME RINGS

Abstract

In this paper we study the notion of (σ, τ)--derivation and prove the following result: Let R be a -prime ring with characteristic different from two and Z(R) be the center of R. If R admits a non-zero (σ, τ)--derivation d of R, with associated automorphisms σ and τ of R, such that σ, τ and d commute with satisfying [d(U), d(U)]σ,τ = {0}, then R is commutative, where U is an ideal of R such that U = U.