ON GENERALIZED -HIGHER DERIVATIONS AND GENERALIZED -HIGHER DERIVATIONS OF PRIME RINGS | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 53, Issue 2, June 2012, Pages 410-418 | ||
| Authors | ||
| Abdulrahman H. Majeed; Anwar Khaleel Faraj | ||
| Abstract | ||
| Let be a Lie ideal of a 2-torsion free prime ring and be commuting endomorphisms of . In this paper we generalize the main result of M. Ashraf, A. Khan and C. Heatinger on -higher derivation of prime ring to generalized -higher derivation of Lie ideal by introducing the concept of generalized -higher derivation. Under some conditions we prove that a Jordan generalized -higher derivation of is either a generalized -higher derivation of or and every Jordan generalized -higher derivation of is a generalized -higher derivation of . Also, we generalize this result to generalized -higher derivation by introducing the concepts of -higher derivation and generalized -higher derivation. Under some conditions we prove that if is a generalized -higher derivation of , then , for all | ||
| Keywords | ||
| derivation; generalized; higher derivation; Lie ideal; prime ring | ||
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