On (σ, τ)‎-derivations and commutativity of prime and semi prime Γ-rings

Abstract EN

Let R be a Г-ring, and σ, τ be two automorphisms of R.

An additive mapping d from a Γ-ring R into itself is called a (σ,τ)-derivation on R if d(aαb) = d(a)α σ(b) + τ(a)αd(b), holds for all a,b ∈R and α∈Γ.

d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]α = [ ] ( ) holds for all a,b∈R and α∈Γ.

In this paper, we investigate the commutativity of R by the strong commutativity preserving (σ,τ)-derivation d satisfied some properties, when R is prime and semi prime Г-ring.