On a Pair of (σ, τ)-derivations of Semiprime Γ-rings

Let M be a 2-torsion free G-ring satisfying an assumption and let s,t be centralizing epimorphisms on M. Let f and g be (s, t)-derivations on M such that f(x)αx + xαg(x) = 0 for all xÎM, αÎG. Then we prove that f(u)β[x, y]α = g(u)β[x, y]α = 0 for all x, y, uÎM, α,βÎG and f, g map M into its center.Keywords. Epimorphism; Commuting; Map; Centralizing map; α-derivation; (α, β)-derivation; Prime Gamma-ring; Semiprime Gamma-ring© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i3.7659 J. Sci. Res. 3 (3), 525-534 (2011)