JP Journal of Algebra, Number Theory and Applications
Volume 25, Issue 1, Pages 29 - 44
(May 2012)
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TRI-ADDITIVE MAPS AND PERMUTING TRI DERIVATIONS OF G-RINGS
Kalyan Kumar Dey, Akhil Chandra Paul and Isamiddin S. Rakhimov
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Abstract: The objective of this paper is to study Tri-additive maps and permuting Tri-derivations of G-rings. The main result of the paper is written as follows. Let M be a 2, 3-torsion free left -unital G-ring and D be a permuting Tri-additive mapping on M with the trace d.
· If d is skew-commuting on M, then and d is commutative on M.
· If for all then or for a fixed element a of M.
· Let and be traces of permuting Tri-derivations and respectively. If the identity where and holds, then there exists an element p of the extended centroid of M such that for all |
Keywords and phrases: Tri-derivation, semiprime G-ring, commutative ideal, commuting map, permuting map. |
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