On the Trace of a Permuting Tri-additive Mapping in Left sγ-unital Γ-rings - Dey, K. K.; Paul, A. C. (Journal of Scientific Research, 2011)
Let M be 2 and 3 torsion-free left sΓ-unital Γ-rings. Let D: M ×M ×M ® M be a permuting tri-additive mapping with the trace d(x) = D(x,x,x). Let σ: M ® M be an endomorphism and τ: M ® M an epimorphism. The objective of this paper is to prove the following: a) If d is (σ,τ)-skew commuting on M, then D = 0; b) If d is (τ,τ)-skew-centralizing on M, then d is (τ,τ)-commuting on M; c) If d is 2-(σ,τ)-commuting on M, then d is (σ,τ)-commuting on M. Keywords: Permuting tri-additive mappings; Skew-commuting mappings; Skew-centralizing mappings; Commuting mappings. © 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi:10.3329/jsr.v3i2.7278 J. Sci. Res. 3 (2), 331-337 (2011)