Abstract
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 = [a,b]α(σ,τ) 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.
Keywords
Prime Г-ring, Semi prime Г-ring, (σ, τ)-derivation, Strong commutativity preserving (σ, τ)-derivation, Commutativity.
Article Type
Article
How to Cite this Article
Ibraheem, Afrah Mohammad
(2016)
"On (σ,τ)-Derivations and Commutativity of Prime and Semi prime Γ-rings,"
Baghdad Science Journal: Vol. 13:
Iss.
1, Article 22.
DOI: https://doi.org/10.21123/bsj.2016.13.1.0198