Open AccessOn a Pair of (σ, τ)-derivations of Semiprime Γ-rings
Author(s) -
Kalyan Kumar Dey,
Akhil Chandra Paul
Publication year - 2011
Publication title -
journal of scientific research
Language(s) - English
Resource type - Journals
eISSN - 2070-0245
pISSN - 2070-0237
DOI - 10.3329/jsr.v3i3.7659
Subject(s) - epimorphism , semiprime ring , mathematics , ring (chemistry) , combinatorics , prime (order theory) , stereochemistry , pure mathematics , chemistry , organic chemistry
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.v3i3.7659J. Sci. Res. 3 (3), 525-534 (2011)