On a Pair of (σ, τ)-derivations of Semiprime Γ-rings
Keywords:Epimorphism, Commuting, Map, Centralizing map, alpha-derivation, (alpha, beta)-derivation, Prime Gamma-ring, Semiprime Gamma-ring.
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)
How to Cite
© Journal of Scientific Research
Articles published in the "Journal of Scientific Research" are Open Access articles under a Creative Commons Attribution-ShareAlike 4.0 International license (CC BY-SA 4.0). This license permits use, distribution and reproduction in any medium, provided the original work is properly cited and initial publication in this journal. In addition to that, users must provide a link to the license, indicate if changes are made and distribute using the same license as original if the original content has been remixed, transformed or built upon.