Permuting Tri-Derivations of Semiprime Gamma Rings

We study some properties of permuting tri-derivations on semiprime G-rings with a certain assumption. Let M be a 3-torsion free semiprime G-ring satisfying a certain assumption and let I be a non-zero ideal of M . Suppose that there exists a permuting tri-derivation D : M × M ´ M → M such that d is an automorphism commuting on I and also d is a trace of D . Then we prove that I is a nonzero commutative ideal. Various characterizations of M are obtained by means of tri-derivations. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v5i1.9549 J. Sci. Res. 5 (1), 55-66 (2013)